Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(53,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.x (of order \(4\), degree \(2\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 53.2 | ||
Character | \(\chi\) | \(=\) | 360.53 |
Dual form | 360.2.x.a.197.2 |
$q$-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 \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37774 | − | 0.319115i | −0.974209 | − | 0.225649i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.79633 | + | 0.879316i | 0.898165 | + | 0.439658i | ||||
\(5\) | 1.42597 | − | 1.72238i | 0.637714 | − | 0.770273i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.11972 | − | 3.11972i | 1.17914 | − | 1.17914i | 0.199179 | − | 0.979963i | \(-0.436172\pi\) |
0.979963 | − | 0.199179i | \(-0.0638277\pi\) | |||||||
\(8\) | −2.19427 | − | 1.78470i | −0.775792 | − | 0.630988i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.51426 | + | 1.91795i | −0.795078 | + | 0.606508i | ||||
\(11\) | −1.17794 | −0.355163 | −0.177581 | − | 0.984106i | \(-0.556827\pi\) | ||||
−0.177581 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.15100 | + | 2.15100i | −0.596579 | + | 0.596579i | −0.939401 | − | 0.342822i | \(-0.888617\pi\) |
0.342822 | + | 0.939401i | \(0.388617\pi\) | |||||||
\(14\) | −5.29371 | + | 3.30261i | −1.41480 | + | 0.882659i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.45361 | + | 3.15908i | 0.613402 | + | 0.789771i | ||||
\(17\) | −1.33507 | − | 1.33507i | −0.323803 | − | 0.323803i | 0.526421 | − | 0.850224i | \(-0.323534\pi\) |
−0.850224 | + | 0.526421i | \(0.823534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.322444 | −0.0739738 | −0.0369869 | − | 0.999316i | \(-0.511776\pi\) | ||||
−0.0369869 | + | 0.999316i | \(0.511776\pi\) | |||||||
\(20\) | 4.07604 | − | 1.84009i | 0.911429 | − | 0.411457i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.62290 | + | 0.375899i | 0.346003 | + | 0.0801420i | ||||
\(23\) | 4.71347 | − | 4.71347i | 0.982826 | − | 0.982826i | −0.0170294 | − | 0.999855i | \(-0.505421\pi\) |
0.999855 | + | 0.0170294i | \(0.00542088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.933209 | − | 4.91214i | −0.186642 | − | 0.982428i | ||||
\(26\) | 3.64993 | − | 2.27710i | 0.715810 | − | 0.446575i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.34726 | − | 2.86083i | 1.57748 | − | 0.540646i | ||||
\(29\) | 6.63043i | 1.23124i | 0.788043 | + | 0.615620i | \(0.211094\pi\) | ||||
−0.788043 | + | 0.615620i | \(0.788906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0675826 | −0.0121382 | −0.00606909 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00606909 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(32\) | −2.37232 | − | 5.13538i | −0.419371 | − | 0.907815i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.41334 | + | 2.26543i | 0.242386 | + | 0.388518i | ||||
\(35\) | −0.924721 | − | 9.82198i | −0.156306 | − | 1.66022i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.60938 | − | 7.60938i | −1.25097 | − | 1.25097i | −0.955284 | − | 0.295690i | \(-0.904450\pi\) |
−0.295690 | − | 0.955284i | \(-0.595550\pi\) | |||||||
\(38\) | 0.444244 | + | 0.102897i | 0.0720659 | + | 0.0166921i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.20292 | + | 1.23444i | −0.980767 | + | 0.195182i | ||||
\(41\) | 3.19684i | 0.499262i | 0.968341 | + | 0.249631i | \(0.0803093\pi\) | ||||
−0.968341 | + | 0.249631i | \(0.919691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.70505 | − | 6.70505i | 1.02251 | − | 1.02251i | 0.0227703 | − | 0.999741i | \(-0.492751\pi\) |
0.999741 | − | 0.0227703i | \(-0.00724865\pi\) | |||||||
\(44\) | −2.11597 | − | 1.03578i | −0.318995 | − | 0.156150i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.99807 | + | 4.98979i | −1.17925 | + | 0.735704i | ||||
\(47\) | 7.34279 | + | 7.34279i | 1.07106 | + | 1.07106i | 0.997274 | + | 0.0737817i | \(0.0235068\pi\) |
0.0737817 | + | 0.997274i | \(0.476493\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12.4653i | − | 1.78075i | ||||||
\(50\) | −0.281821 | + | 7.06545i | −0.0398555 | + | 0.999205i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.75531 | + | 1.97250i | −0.798117 | + | 0.273536i | ||||
\(53\) | 5.73432 | + | 5.73432i | 0.787669 | + | 0.787669i | 0.981112 | − | 0.193442i | \(-0.0619653\pi\) |
−0.193442 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67971 | + | 2.02887i | −0.226492 | + | 0.273572i | ||||
\(56\) | −12.4133 | + | 1.27774i | −1.65879 | + | 0.170745i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.11587 | − | 9.13501i | 0.277828 | − | 1.19949i | ||||
\(59\) | − | 8.68448i | − | 1.13062i | −0.824877 | − | 0.565312i | \(-0.808756\pi\) | ||
0.824877 | − | 0.565312i | \(-0.191244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5620i | 1.60840i | 0.594359 | + | 0.804199i | \(0.297406\pi\) | ||||
−0.594359 | + | 0.804199i | \(0.702594\pi\) | |||||||
\(62\) | 0.0931112 | + | 0.0215666i | 0.0118251 | + | 0.00273897i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.62966 | + | 7.83225i | 0.203708 | + | 0.979032i | ||||
\(65\) | 0.637580 | + | 6.77210i | 0.0790821 | + | 0.839976i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.87740 | − | 1.87740i | −0.229360 | − | 0.229360i | 0.583065 | − | 0.812425i | \(-0.301853\pi\) |
−0.812425 | + | 0.583065i | \(0.801853\pi\) | |||||||
\(68\) | −1.22428 | − | 3.57219i | −0.148466 | − | 0.433191i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.86032 | + | 13.8272i | −0.222351 | + | 1.65267i | ||||
\(71\) | − | 4.18221i | − | 0.496337i | −0.968717 | − | 0.248168i | \(-0.920171\pi\) | ||
0.968717 | − | 0.248168i | \(-0.0798286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97893 | + | 3.97893i | 0.465699 | + | 0.465699i | 0.900518 | − | 0.434819i | \(-0.143188\pi\) |
−0.434819 | + | 0.900518i | \(0.643188\pi\) | |||||||
\(74\) | 8.05547 | + | 12.9120i | 0.936429 | + | 1.50099i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.579216 | − | 0.283530i | −0.0664407 | − | 0.0325231i | ||||
\(77\) | −3.67485 | + | 3.67485i | −0.418788 | + | 0.418788i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.66644i | 1.08756i | 0.839228 | + | 0.543780i | \(0.183007\pi\) | ||||
−0.839228 | + | 0.543780i | \(0.816993\pi\) | |||||||
\(80\) | 8.93993 | + | 0.278710i | 0.999514 | + | 0.0311607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.02016 | − | 4.40441i | 0.112658 | − | 0.486385i | ||||
\(83\) | −0.585119 | − | 0.585119i | −0.0642251 | − | 0.0642251i | 0.674265 | − | 0.738490i | \(-0.264461\pi\) |
−0.738490 | + | 0.674265i | \(0.764461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.20329 | + | 0.395732i | −0.455911 | + | 0.0429231i | ||||
\(86\) | −11.3775 | + | 7.09813i | −1.22687 | + | 0.765411i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.58473 | + | 2.10228i | 0.275533 | + | 0.224104i | ||||
\(89\) | 0.557322 | 0.0590760 | 0.0295380 | − | 0.999564i | \(-0.490596\pi\) | ||||
0.0295380 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.4210i | 1.40690i | ||||||||
\(92\) | 12.6116 | − | 4.32232i | 1.31485 | − | 0.450633i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.77325 | − | 12.4596i | −0.801750 | − | 1.28511i | ||||
\(95\) | −0.459796 | + | 0.555372i | −0.0471741 | + | 0.0569800i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5772 | + | 10.5772i | −1.07395 | + | 1.07395i | −0.0769138 | + | 0.997038i | \(0.524507\pi\) |
−0.997038 | + | 0.0769138i | \(0.975493\pi\) | |||||||
\(98\) | −3.97786 | + | 17.1739i | −0.401825 | + | 1.73483i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.64297 | − | 9.64441i | 0.264297 | − | 0.964441i | ||||
\(101\) | 9.52870 | 0.948141 | 0.474071 | − | 0.880487i | \(-0.342784\pi\) | ||||
0.474071 | + | 0.880487i | \(0.342784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.162450 | − | 0.162450i | −0.0160066 | − | 0.0160066i | 0.699058 | − | 0.715065i | \(-0.253603\pi\) |
−0.715065 | + | 0.699058i | \(0.753603\pi\) | |||||||
\(104\) | 8.55876 | − | 0.880979i | 0.839256 | − | 0.0863871i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.07049 | − | 9.73030i | −0.589618 | − | 0.945091i | ||||
\(107\) | −11.7955 | + | 11.7955i | −1.14032 | + | 1.14032i | −0.151925 | + | 0.988392i | \(0.548547\pi\) |
−0.988392 | + | 0.151925i | \(0.951453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8601 | 1.04021 | 0.520105 | − | 0.854102i | \(-0.325893\pi\) | ||||
0.520105 | + | 0.854102i | \(0.325893\pi\) | |||||||
\(110\) | 2.96165 | − | 2.25923i | 0.282382 | − | 0.215409i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17.5100 | + | 2.20088i | 1.65454 | + | 0.207964i | ||||
\(113\) | −8.74476 | + | 8.74476i | −0.822637 | + | 0.822637i | −0.986486 | − | 0.163848i | \(-0.947609\pi\) |
0.163848 | + | 0.986486i | \(0.447609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39713 | − | 14.8397i | −0.130283 | − | 1.38381i | ||||
\(116\) | −5.83024 | + | 11.9105i | −0.541325 | + | 1.10586i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.77135 | + | 11.9650i | −0.255124 | + | 1.10146i | ||||
\(119\) | −8.33011 | −0.763620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.61245 | −0.873859 | ||||||||
\(122\) | 4.00873 | − | 17.3072i | 0.362933 | − | 1.56692i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.121401 | − | 0.0594264i | −0.0109021 | − | 0.00533665i | ||||
\(125\) | −9.79132 | − | 5.39723i | −0.875762 | − | 0.482743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.83755 | + | 3.83755i | −0.340528 | + | 0.340528i | −0.856566 | − | 0.516038i | \(-0.827406\pi\) |
0.516038 | + | 0.856566i | \(0.327406\pi\) | |||||||
\(128\) | 0.254145 | − | 11.3109i | 0.0224635 | − | 0.999748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.28266 | − | 9.53365i | 0.112497 | − | 0.836156i | ||||
\(131\) | 1.85715 | 0.162260 | 0.0811298 | − | 0.996704i | \(-0.474147\pi\) | ||||
0.0811298 | + | 0.996704i | \(0.474147\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00593 | + | 1.00593i | −0.0872256 | + | 0.0872256i | ||||
\(134\) | 1.98746 | + | 3.18567i | 0.171690 | + | 0.275200i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.546804 | + | 5.31223i | 0.0468880 | + | 0.455520i | ||||
\(137\) | −1.89240 | − | 1.89240i | −0.161678 | − | 0.161678i | 0.621631 | − | 0.783310i | \(-0.286470\pi\) |
−0.783310 | + | 0.621631i | \(0.786470\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4370 | 1.56380 | 0.781902 | − | 0.623401i | \(-0.214250\pi\) | ||||
0.781902 | + | 0.623401i | \(0.214250\pi\) | |||||||
\(140\) | 6.97552 | − | 18.4566i | 0.589539 | − | 1.55987i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.33461 | + | 5.76199i | −0.111998 | + | 0.483536i | ||||
\(143\) | 2.53375 | − | 2.53375i | 0.211883 | − | 0.211883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4201 | + | 9.45481i | 0.948392 | + | 0.785179i | ||||
\(146\) | −4.21219 | − | 6.75167i | −0.348603 | − | 0.558772i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.97791 | − | 20.3600i | −0.573581 | − | 1.67358i | ||||
\(149\) | 1.24573i | 0.102054i | 0.998697 | + | 0.0510272i | \(0.0162495\pi\) | ||||
−0.998697 | + | 0.0510272i | \(0.983750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.7587 | 1.36380 | 0.681902 | − | 0.731444i | \(-0.261153\pi\) | ||||
0.681902 | + | 0.731444i | \(0.261153\pi\) | |||||||
\(152\) | 0.707530 | + | 0.575468i | 0.0573883 | + | 0.0466766i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.23568 | − | 3.89028i | 0.502485 | − | 0.313488i | ||||
\(155\) | −0.0963708 | + | 0.116403i | −0.00774069 | + | 0.00934972i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.90784 | − | 6.90784i | −0.551306 | − | 0.551306i | 0.375512 | − | 0.926818i | \(-0.377467\pi\) |
−0.926818 | + | 0.375512i | \(0.877467\pi\) | |||||||
\(158\) | 3.08471 | − | 13.3178i | 0.245406 | − | 1.05951i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.2279 | − | 3.23686i | −0.966704 | − | 0.255896i | ||||
\(161\) | − | 29.4094i | − | 2.31778i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.07821 | + | 6.07821i | −0.476082 | + | 0.476082i | −0.903876 | − | 0.427794i | \(-0.859291\pi\) |
0.427794 | + | 0.903876i | \(0.359291\pi\) | |||||||
\(164\) | −2.81103 | + | 5.74257i | −0.219504 | + | 0.448420i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.619421 | + | 0.992861i | 0.0480764 | + | 0.0770610i | ||||
\(167\) | −2.82159 | − | 2.82159i | −0.218341 | − | 0.218341i | 0.589458 | − | 0.807799i | \(-0.299341\pi\) |
−0.807799 | + | 0.589458i | \(0.799341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.74643i | 0.288187i | ||||||||
\(170\) | 5.91732 | + | 0.796119i | 0.453838 | + | 0.0610596i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.9404 | − | 6.14864i | 1.36794 | − | 0.468829i | ||||
\(173\) | 7.27921 | + | 7.27921i | 0.553428 | + | 0.553428i | 0.927428 | − | 0.374001i | \(-0.122014\pi\) |
−0.374001 | + | 0.927428i | \(0.622014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.2358 | − | 12.4131i | −1.37850 | − | 0.938345i | ||||
\(176\) | −2.89021 | − | 3.72122i | −0.217858 | − | 0.280497i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.767845 | − | 0.177850i | −0.0575524 | − | 0.0133304i | ||||
\(179\) | − | 9.56604i | − | 0.714999i | −0.933913 | − | 0.357500i | \(-0.883629\pi\) | ||
0.933913 | − | 0.357500i | \(-0.116371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.44857i | − | 0.330659i | −0.986238 | − | 0.165330i | \(-0.947131\pi\) | ||
0.986238 | − | 0.165330i | \(-0.0528688\pi\) | |||||||
\(182\) | 4.28285 | − | 18.4906i | 0.317466 | − | 1.37062i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.7548 | + | 1.93048i | −1.38262 | + | 0.142317i | ||||
\(185\) | −23.9570 | + | 2.25551i | −1.76136 | + | 0.165828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.57264 | + | 1.57264i | 0.115003 | + | 0.115003i | ||||
\(188\) | 6.73345 | + | 19.6467i | 0.491087 | + | 1.43288i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.810707 | − | 0.618430i | 0.0588149 | − | 0.0448657i | ||||
\(191\) | 3.16704i | 0.229159i | 0.993414 | + | 0.114579i | \(0.0365521\pi\) | ||||
−0.993414 | + | 0.114579i | \(0.963448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07726 | + | 1.07726i | 0.0775426 | + | 0.0775426i | 0.744814 | − | 0.667272i | \(-0.232538\pi\) |
−0.667272 | + | 0.744814i | \(0.732538\pi\) | |||||||
\(194\) | 17.9480 | − | 11.1973i | 1.28859 | − | 0.803917i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.9609 | − | 22.3918i | 0.782922 | − | 1.59941i | ||||
\(197\) | −5.59062 | + | 5.59062i | −0.398315 | + | 0.398315i | −0.877638 | − | 0.479323i | \(-0.840882\pi\) |
0.479323 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7707i | 1.11796i | 0.829182 | + | 0.558978i | \(0.188806\pi\) | ||||
−0.829182 | + | 0.558978i | \(0.811194\pi\) | |||||||
\(200\) | −6.71900 | + | 12.4441i | −0.475105 | + | 0.879929i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.1281 | − | 3.04076i | −0.923688 | − | 0.213947i | ||||
\(203\) | 20.6851 | + | 20.6851i | 1.45181 | + | 1.45181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.50618 | + | 4.55860i | 0.384568 | + | 0.318386i | ||||
\(206\) | 0.171973 | + | 0.275653i | 0.0119819 | + | 0.0192057i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0729 | − | 1.51747i | −0.837104 | − | 0.105218i | ||||
\(209\) | 0.379820 | 0.0262727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9274i | 0.752273i | 0.926564 | + | 0.376137i | \(0.122748\pi\) | ||||
−0.926564 | + | 0.376137i | \(0.877252\pi\) | |||||||
\(212\) | 5.25846 | + | 15.3430i | 0.361152 | + | 1.05376i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.0153 | − | 12.4870i | 1.36822 | − | 0.853596i | ||||
\(215\) | −1.98746 | − | 21.1099i | −0.135543 | − | 1.43968i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.210839 | + | 0.210839i | −0.0143127 | + | 0.0143127i | ||||
\(218\) | −14.9624 | − | 3.46563i | −1.01338 | − | 0.234722i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.80133 | + | 2.16752i | −0.323706 | + | 0.146134i | ||||
\(221\) | 5.74348 | 0.386348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.947865 | + | 0.947865i | 0.0634737 | + | 0.0634737i | 0.738131 | − | 0.674657i | \(-0.235709\pi\) |
−0.674657 | + | 0.738131i | \(0.735709\pi\) | |||||||
\(224\) | −23.4219 | − | 8.61996i | −1.56494 | − | 0.575945i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.8386 | − | 9.25741i | 0.987048 | − | 0.615794i | ||||
\(227\) | 4.87410 | − | 4.87410i | 0.323506 | − | 0.323506i | −0.526605 | − | 0.850110i | \(-0.676535\pi\) |
0.850110 | + | 0.526605i | \(0.176535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1740 | 1.13489 | 0.567444 | − | 0.823412i | \(-0.307932\pi\) | ||||
0.567444 | + | 0.823412i | \(0.307932\pi\) | |||||||
\(230\) | −2.81069 | + | 20.8910i | −0.185331 | + | 1.37751i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.8334 | − | 14.5490i | 0.776898 | − | 0.955187i | ||||
\(233\) | 17.1696 | − | 17.1696i | 1.12482 | − | 1.12482i | 0.133811 | − | 0.991007i | \(-0.457278\pi\) |
0.991007 | − | 0.133811i | \(-0.0427216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1177 | − | 2.17649i | 1.50803 | − | 0.141978i | ||||
\(236\) | 7.63640 | − | 15.6002i | 0.497087 | − | 1.01549i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.4767 | + | 2.65827i | 0.743926 | + | 0.172310i | ||||
\(239\) | −19.8347 | −1.28300 | −0.641501 | − | 0.767122i | \(-0.721688\pi\) | ||||
−0.641501 | + | 0.767122i | \(0.721688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.89615 | −0.186557 | −0.0932787 | − | 0.995640i | \(-0.529735\pi\) | ||||
−0.0932787 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(242\) | 13.2435 | + | 3.06748i | 0.851321 | + | 0.197185i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.0460 | + | 22.5655i | −0.707145 | + | 1.44461i | ||||
\(245\) | −21.4700 | − | 17.7751i | −1.37167 | − | 1.13561i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.693576 | − | 0.693576i | 0.0441312 | − | 0.0441312i | ||||
\(248\) | 0.148295 | + | 0.120615i | 0.00941671 | + | 0.00765905i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.7675 | + | 10.5605i | 0.744245 | + | 0.667907i | ||||
\(251\) | −8.93270 | −0.563827 | −0.281914 | − | 0.959440i | \(-0.590969\pi\) | ||||
−0.281914 | + | 0.959440i | \(0.590969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.55219 | + | 5.55219i | −0.349063 | + | 0.349063i | ||||
\(254\) | 6.51177 | − | 4.06252i | 0.408584 | − | 0.254905i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.95961 | + | 15.5023i | −0.247476 | + | 0.968894i | ||||
\(257\) | 12.4301 | + | 12.4301i | 0.775367 | + | 0.775367i | 0.979039 | − | 0.203672i | \(-0.0652877\pi\) |
−0.203672 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −47.4782 | −2.95015 | ||||||||
\(260\) | −4.80951 | + | 12.7256i | −0.298273 | + | 0.789206i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.55866 | − | 0.592644i | −0.158075 | − | 0.0366137i | ||||
\(263\) | −12.1529 | + | 12.1529i | −0.749383 | + | 0.749383i | −0.974363 | − | 0.224981i | \(-0.927768\pi\) |
0.224981 | + | 0.974363i | \(0.427768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0537 | − | 1.69972i | 1.10903 | − | 0.104413i | ||||
\(266\) | 1.70693 | − | 1.06491i | 0.104658 | − | 0.0652936i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.72160 | − | 5.02325i | −0.105163 | − | 0.306844i | ||||
\(269\) | − | 19.0912i | − | 1.16401i | −0.813185 | − | 0.582005i | \(-0.802268\pi\) | ||
0.813185 | − | 0.582005i | \(-0.197732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6087 | 0.826670 | 0.413335 | − | 0.910579i | \(-0.364364\pi\) | ||||
0.413335 | + | 0.910579i | \(0.364364\pi\) | |||||||
\(272\) | 0.941862 | − | 7.49336i | 0.0571088 | − | 0.454352i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00334 | + | 3.21112i | 0.121026 | + | 0.193991i | ||||
\(275\) | 1.09927 | + | 5.78622i | 0.0662882 | + | 0.348922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9103 | + | 13.9103i | 0.835788 | + | 0.835788i | 0.988301 | − | 0.152514i | \(-0.0487368\pi\) |
−0.152514 | + | 0.988301i | \(0.548737\pi\) | |||||||
\(278\) | −25.4014 | − | 5.88353i | −1.52347 | − | 0.352870i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.5002 | + | 23.2024i | −0.926317 | + | 1.38661i | ||||
\(281\) | 13.9435i | 0.831799i | 0.909411 | + | 0.415899i | \(0.136533\pi\) | ||||
−0.909411 | + | 0.415899i | \(0.863467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.3526 | + | 14.3526i | −0.853174 | + | 0.853174i | −0.990523 | − | 0.137349i | \(-0.956142\pi\) |
0.137349 | + | 0.990523i | \(0.456142\pi\) | |||||||
\(284\) | 3.67748 | − | 7.51263i | 0.218218 | − | 0.445793i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.29940 | + | 2.68229i | −0.254229 | + | 0.158607i | ||||
\(287\) | 9.97323 | + | 9.97323i | 0.588701 | + | 0.588701i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.4352i | − | 0.790303i | ||||||
\(290\) | −12.7168 | − | 16.6706i | −0.746757 | − | 0.978932i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.64874 | + | 10.6462i | 0.213526 | + | 0.623022i | ||||
\(293\) | −12.4180 | − | 12.4180i | −0.725465 | − | 0.725465i | 0.244248 | − | 0.969713i | \(-0.421459\pi\) |
−0.969713 | + | 0.244248i | \(0.921459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.9580 | − | 12.3838i | −0.870889 | − | 0.721014i | ||||
\(296\) | 3.11656 | + | 30.2775i | 0.181146 | + | 1.75985i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.397533 | − | 1.71630i | 0.0230285 | − | 0.0994224i | ||||
\(299\) | 20.2773i | 1.17267i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 41.8357i | − | 2.41137i | ||||||
\(302\) | −23.0891 | − | 5.34796i | −1.32863 | − | 0.307740i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.791152 | − | 1.01863i | −0.0453757 | − | 0.0584223i | ||||
\(305\) | 21.6366 | + | 17.9131i | 1.23891 | + | 1.02570i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9940 | − | 14.9940i | −0.855753 | − | 0.855753i | 0.135082 | − | 0.990834i | \(-0.456870\pi\) |
−0.990834 | + | 0.135082i | \(0.956870\pi\) | |||||||
\(308\) | −9.83259 | + | 3.36989i | −0.560264 | + | 0.192017i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.169920 | − | 0.129620i | 0.00965080 | − | 0.00736190i | ||||
\(311\) | 32.7316i | 1.85604i | 0.372534 | + | 0.928019i | \(0.378489\pi\) | ||||
−0.372534 | + | 0.928019i | \(0.621511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.25286 | + | 8.25286i | 0.466479 | + | 0.466479i | 0.900772 | − | 0.434293i | \(-0.143002\pi\) |
−0.434293 | + | 0.900772i | \(0.643002\pi\) | |||||||
\(314\) | 7.31281 | + | 11.7216i | 0.412686 | + | 0.661488i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.49985 | + | 17.3641i | −0.478154 | + | 0.976808i | ||||
\(317\) | 8.30940 | − | 8.30940i | 0.466702 | − | 0.466702i | −0.434142 | − | 0.900844i | \(-0.642948\pi\) |
0.900844 | + | 0.434142i | \(0.142948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.81027i | − | 0.437291i | ||||||
\(320\) | 15.8140 | + | 8.36167i | 0.884029 | + | 0.467432i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.38498 | + | 40.5184i | −0.523005 | + | 2.25800i | ||||
\(323\) | 0.430487 | + | 0.430487i | 0.0239529 | + | 0.0239529i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5733 | + | 8.55867i | 0.697443 | + | 0.474749i | ||||
\(326\) | 10.3138 | − | 6.43454i | 0.571231 | − | 0.356376i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.70541 | − | 7.01473i | 0.315028 | − | 0.387324i | ||||
\(329\) | 45.8149 | 2.52586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.43429i | − | 0.408626i | −0.978906 | − | 0.204313i | \(-0.934504\pi\) | ||
0.978906 | − | 0.204313i | \(-0.0654960\pi\) | |||||||
\(332\) | −0.536563 | − | 1.56557i | −0.0294477 | − | 0.0859219i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.98700 | + | 4.78782i | 0.163441 | + | 0.261978i | ||||
\(335\) | −5.91071 | + | 0.556482i | −0.322936 | + | 0.0304038i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.88868 | + | 3.88868i | −0.211830 | + | 0.211830i | −0.805044 | − | 0.593215i | \(-0.797859\pi\) |
0.593215 | + | 0.805044i | \(0.297859\pi\) | |||||||
\(338\) | 1.19554 | − | 5.16160i | 0.0650290 | − | 0.280754i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.89847 | − | 2.98515i | −0.428355 | − | 0.161893i | ||||
\(341\) | 0.0796083 | 0.00431103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0501 | − | 17.0501i | −0.920620 | − | 0.920620i | ||||
\(344\) | −26.6793 | + | 2.74617i | −1.43845 | + | 0.148064i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.70594 | − | 12.3518i | −0.414274 | − | 0.664034i | ||||
\(347\) | −20.7432 | + | 20.7432i | −1.11355 | + | 1.11355i | −0.120889 | + | 0.992666i | \(0.538574\pi\) |
−0.992666 | + | 0.120889i | \(0.961426\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.04055 | 0.162757 | 0.0813783 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813783 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(350\) | 21.1630 | + | 22.9214i | 1.13121 | + | 1.22520i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.79446 | + | 6.04918i | 0.148945 | + | 0.322422i | ||||
\(353\) | −3.46489 | + | 3.46489i | −0.184417 | + | 0.184417i | −0.793278 | − | 0.608860i | \(-0.791627\pi\) |
0.608860 | + | 0.793278i | \(0.291627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.20337 | − | 5.96371i | −0.382315 | − | 0.316521i | ||||
\(356\) | 1.00113 | + | 0.490062i | 0.0530600 | + | 0.0259732i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.05267 | + | 13.1795i | −0.161339 | + | 0.696558i | ||||
\(359\) | 8.63299 | 0.455632 | 0.227816 | − | 0.973704i | \(-0.426842\pi\) | ||||
0.227816 | + | 0.973704i | \(0.426842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8960 | −0.994528 | ||||||||
\(362\) | −1.41961 | + | 6.12897i | −0.0746129 | + | 0.322131i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.8013 | + | 24.1086i | −0.618556 | + | 1.26363i | ||||
\(365\) | 12.5271 | − | 1.17940i | 0.655698 | − | 0.0617327i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3844 | − | 15.3844i | 0.803060 | − | 0.803060i | −0.180512 | − | 0.983573i | \(-0.557776\pi\) |
0.983573 | + | 0.180512i | \(0.0577756\pi\) | |||||||
\(368\) | 26.4552 | + | 3.32523i | 1.37907 | + | 0.173340i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.7263 | + | 4.53755i | 1.75335 | + | 0.235896i | ||||
\(371\) | 35.7789 | 1.85755 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.40616 | + | 7.40616i | −0.383476 | + | 0.383476i | −0.872353 | − | 0.488877i | \(-0.837407\pi\) |
0.488877 | + | 0.872353i | \(0.337407\pi\) | |||||||
\(374\) | −1.66483 | − | 2.66854i | −0.0860866 | − | 0.137987i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00737 | − | 29.2168i | −0.155093 | − | 1.50674i | ||||
\(377\) | −14.2620 | − | 14.2620i | −0.734532 | − | 0.734532i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.54952 | −0.336426 | −0.168213 | − | 0.985751i | \(-0.553800\pi\) | ||||
−0.168213 | + | 0.985751i | \(0.553800\pi\) | |||||||
\(380\) | −1.31429 | + | 0.593327i | −0.0674219 | + | 0.0304370i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.01065 | − | 4.36336i | 0.0517094 | − | 0.223249i | ||||
\(383\) | 14.8778 | − | 14.8778i | 0.760222 | − | 0.760222i | −0.216140 | − | 0.976362i | \(-0.569347\pi\) |
0.976362 | + | 0.216140i | \(0.0693468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.08927 | + | 11.5697i | 0.0555142 | + | 0.589648i | ||||
\(386\) | −1.14041 | − | 1.82795i | −0.0580453 | − | 0.0930401i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.3008 | + | 9.69945i | −1.43676 | + | 0.492415i | ||||
\(389\) | − | 0.254115i | − | 0.0128842i | −0.999979 | − | 0.00644208i | \(-0.997949\pi\) | ||
0.999979 | − | 0.00644208i | \(-0.00205059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.5857 | −0.636484 | ||||||||
\(392\) | −22.2468 | + | 27.3522i | −1.12363 | + | 1.38150i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.48647 | − | 5.91836i | 0.477921 | − | 0.298163i | ||||
\(395\) | 16.6493 | + | 13.7841i | 0.837718 | + | 0.693552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6584 | − | 20.6584i | −1.03682 | − | 1.03682i | −0.999296 | − | 0.0375215i | \(-0.988054\pi\) |
−0.0375215 | − | 0.999296i | \(-0.511946\pi\) | |||||||
\(398\) | 5.03268 | − | 21.7279i | 0.252265 | − | 1.08912i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2281 | − | 15.0006i | 0.661407 | − | 0.750028i | ||||
\(401\) | − | 20.6863i | − | 1.03303i | −0.856279 | − | 0.516513i | \(-0.827230\pi\) | ||
0.856279 | − | 0.516513i | \(-0.172770\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.145370 | − | 0.145370i | 0.00724139 | − | 0.00724139i | ||||
\(404\) | 17.1167 | + | 8.37874i | 0.851588 | + | 0.416858i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.8977 | − | 35.0996i | −1.08677 | − | 1.74196i | ||||
\(407\) | 8.96340 | + | 8.96340i | 0.444299 | + | 0.444299i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.9787i | − | 1.33401i | −0.745053 | − | 0.667005i | \(-0.767576\pi\) | ||
0.745053 | − | 0.667005i | \(-0.232424\pi\) | |||||||
\(410\) | −6.13136 | − | 8.03766i | −0.302806 | − | 0.396952i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.148969 | − | 0.434658i | −0.00733916 | − | 0.0214140i | ||||
\(413\) | −27.0931 | − | 27.0931i | −1.33317 | − | 1.33317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.84216 | + | 0.173436i | −0.0904282 | + | 0.00851364i | ||||
\(416\) | 16.1490 | + | 5.94333i | 0.791771 | + | 0.291395i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.523294 | − | 0.121207i | −0.0255951 | − | 0.00592841i | ||||
\(419\) | − | 34.3778i | − | 1.67946i | −0.543001 | − | 0.839732i | \(-0.682712\pi\) | ||
0.543001 | − | 0.839732i | \(-0.317288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.05773i | 0.197762i | 0.995099 | + | 0.0988809i | \(0.0315263\pi\) | ||||
−0.995099 | + | 0.0988809i | \(0.968474\pi\) | |||||||
\(422\) | 3.48710 | − | 15.0551i | 0.169749 | − | 0.732871i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.34859 | − | 22.8167i | −0.114058 | − | 1.10808i | ||||
\(425\) | −5.31217 | + | 7.80398i | −0.257678 | + | 0.378549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.1899 | + | 39.1899i | 1.89653 | + | 1.89653i | ||||
\(428\) | −31.5607 | + | 10.8167i | −1.52554 | + | 0.522844i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.99830 | + | 29.7182i | −0.192815 | + | 1.43314i | ||||
\(431\) | − | 16.0853i | − | 0.774800i | −0.921912 | − | 0.387400i | \(-0.873373\pi\) | ||
0.921912 | − | 0.387400i | \(-0.126627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.04812 | − | 3.04812i | −0.146483 | − | 0.146483i | 0.630062 | − | 0.776545i | \(-0.283030\pi\) |
−0.776545 | + | 0.630062i | \(0.783030\pi\) | |||||||
\(434\) | 0.357762 | − | 0.223199i | 0.0171731 | − | 0.0107139i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.5084 | + | 9.54947i | 0.934281 | + | 0.457337i | ||||
\(437\) | −1.51983 | + | 1.51983i | −0.0727033 | + | 0.0727033i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.78470i | − | 0.228361i | −0.993460 | − | 0.114181i | \(-0.963576\pi\) | ||
0.993460 | − | 0.114181i | \(-0.0364243\pi\) | |||||||
\(440\) | 7.30667 | − | 1.45410i | 0.348332 | − | 0.0693214i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.91302 | − | 1.83283i | −0.376384 | − | 0.0871790i | ||||
\(443\) | −11.2608 | − | 11.2608i | −0.535019 | − | 0.535019i | 0.387043 | − | 0.922062i | \(-0.373497\pi\) |
−0.922062 | + | 0.387043i | \(0.873497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.794726 | − | 0.959922i | 0.0376736 | − | 0.0455047i | ||||
\(446\) | −1.00343 | − | 1.60839i | −0.0475139 | − | 0.0761594i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.5185 | + | 19.3503i | 1.39462 | + | 0.914218i | ||||
\(449\) | −7.49133 | −0.353538 | −0.176769 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176769 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.76569i | − | 0.177319i | ||||||
\(452\) | −23.3979 | + | 8.01907i | −1.10054 | + | 0.377185i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.27065 | + | 5.15984i | −0.388161 | + | 0.242163i | ||||
\(455\) | 23.1161 | + | 19.1380i | 1.08370 | + | 0.897202i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2198 | + | 14.2198i | −0.665173 | + | 0.665173i | −0.956595 | − | 0.291422i | \(-0.905872\pi\) |
0.291422 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(458\) | −23.6613 | − | 5.48048i | −1.10562 | − | 0.256086i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.5390 | − | 27.8855i | 0.491386 | − | 1.30017i | ||||
\(461\) | 19.4366 | 0.905254 | 0.452627 | − | 0.891700i | \(-0.350487\pi\) | ||||
0.452627 | + | 0.891700i | \(0.350487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.18789 | − | 2.18789i | −0.101680 | − | 0.101680i | 0.654437 | − | 0.756117i | \(-0.272906\pi\) |
−0.756117 | + | 0.654437i | \(0.772906\pi\) | |||||||
\(464\) | −20.9461 | + | 16.2685i | −0.972398 | + | 0.755246i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.1343 | + | 18.1762i | −1.34962 | + | 0.841994i | ||||
\(467\) | 2.06992 | − | 2.06992i | 0.0957845 | − | 0.0957845i | −0.657591 | − | 0.753375i | \(-0.728424\pi\) |
0.753375 | + | 0.657591i | \(0.228424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7139 | −0.540897 | ||||||||
\(470\) | −32.5447 | − | 4.37858i | −1.50118 | − | 0.201969i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4992 | + | 19.0561i | −0.713410 | + | 0.877129i | ||||
\(473\) | −7.89816 | + | 7.89816i | −0.363158 | + | 0.363158i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.300908 | + | 1.58389i | 0.0138066 | + | 0.0726739i | ||||
\(476\) | −14.9636 | − | 7.32480i | −0.685857 | − | 0.335732i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.3271 | + | 6.32957i | 1.24991 | + | 0.289508i | ||||
\(479\) | −27.5481 | −1.25871 | −0.629353 | − | 0.777120i | \(-0.716680\pi\) | ||||
−0.629353 | + | 0.777120i | \(0.716680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.7355 | 1.49261 | ||||||||
\(482\) | 3.99014 | + | 0.924206i | 0.181746 | + | 0.0420964i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.2671 | − | 8.45238i | −0.784870 | − | 0.384199i | ||||
\(485\) | 3.13520 | + | 33.3008i | 0.142362 | + | 1.51211i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7336 | − | 27.7336i | 1.25673 | − | 1.25673i | 0.304083 | − | 0.952646i | \(-0.401650\pi\) |
0.952646 | − | 0.304083i | \(-0.0983500\pi\) | |||||||
\(488\) | 22.4195 | − | 27.5644i | 1.01488 | − | 1.24778i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23.9077 | + | 31.3409i | 1.08004 | + | 1.41584i | ||||
\(491\) | −2.58679 | −0.116740 | −0.0583700 | − | 0.998295i | \(-0.518590\pi\) | ||||
−0.0583700 | + | 0.998295i | \(0.518590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.85213 | − | 8.85213i | 0.398680 | − | 0.398680i | ||||
\(494\) | −1.17690 | + | 0.734236i | −0.0529511 | + | 0.0330349i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.165821 | − | 0.213499i | −0.00744559 | − | 0.00958639i | ||||
\(497\) | −13.0473 | − | 13.0473i | −0.585252 | − | 0.585252i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.5951 | −1.14579 | −0.572897 | − | 0.819627i | \(-0.694181\pi\) | ||||
−0.572897 | + | 0.819627i | \(0.694181\pi\) | |||||||
\(500\) | −12.8426 | − | 18.3049i | −0.574338 | − | 0.818619i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.3069 | + | 2.85056i | 0.549285 | + | 0.127227i | ||||
\(503\) | 9.39909 | − | 9.39909i | 0.419085 | − | 0.419085i | −0.465804 | − | 0.884888i | \(-0.654235\pi\) |
0.884888 | + | 0.465804i | \(0.154235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5877 | − | 16.4121i | 0.604643 | − | 0.730328i | ||||
\(506\) | 9.42126 | − | 5.87768i | 0.418826 | − | 0.261295i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.2679 | + | 3.51909i | −0.455566 | + | 0.156134i | ||||
\(509\) | 11.5075i | 0.510059i | 0.966933 | + | 0.255030i | \(0.0820852\pi\) | ||||
−0.966933 | + | 0.255030i | \(0.917915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.8263 | 1.09825 | ||||||||
\(512\) | 10.4023 | − | 20.0946i | 0.459723 | − | 0.888062i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1588 | − | 21.0920i | −0.580409 | − | 0.930329i | ||||
\(515\) | −0.511449 | + | 0.0481519i | −0.0225371 | + | 0.00212183i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.64938 | − | 8.64938i | −0.380399 | − | 0.380399i | ||||
\(518\) | 65.4126 | + | 15.1510i | 2.87406 | + | 0.665698i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.6872 | − | 15.9977i | 0.468664 | − | 0.701547i | ||||
\(521\) | 8.12668i | 0.356036i | 0.984027 | + | 0.178018i | \(0.0569686\pi\) | ||||
−0.984027 | + | 0.178018i | \(0.943031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.2646 | − | 23.2646i | 1.01729 | − | 1.01729i | 0.0174440 | − | 0.999848i | \(-0.494447\pi\) |
0.999848 | − | 0.0174440i | \(-0.00555287\pi\) | |||||||
\(524\) | 3.33605 | + | 1.63302i | 0.145736 | + | 0.0713387i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.6218 | − | 12.8654i | 0.899152 | − | 0.560958i | ||||
\(527\) | 0.0902278 | + | 0.0902278i | 0.00393038 | + | 0.00393038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.4335i | − | 0.931892i | ||||||
\(530\) | −25.4157 | − | 3.41944i | −1.10399 | − | 0.148531i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.69153 | + | 0.922457i | −0.116692 | + | 0.0399936i | ||||
\(533\) | −6.87638 | − | 6.87638i | −0.297849 | − | 0.297849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.49633 | + | 37.1365i | 0.151160 | + | 1.60555i | ||||
\(536\) | 0.768921 | + | 7.47011i | 0.0332123 | + | 0.322660i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.09229 | + | 26.3027i | −0.262657 | + | 1.13399i | ||||
\(539\) | 14.6834i | 0.632458i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6496i | 0.930787i | 0.885104 | + | 0.465393i | \(0.154087\pi\) | ||||
−0.885104 | + | 0.465393i | \(0.845913\pi\) | |||||||
\(542\) | −18.7492 | − | 4.34275i | −0.805349 | − | 0.186537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.68889 | + | 10.0233i | −0.158160 | + | 0.429747i | ||||
\(545\) | 15.4862 | − | 18.7053i | 0.663357 | − | 0.801246i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.4574 | − | 15.4574i | −0.660912 | − | 0.660912i | 0.294683 | − | 0.955595i | \(-0.404786\pi\) |
−0.955595 | + | 0.294683i | \(0.904786\pi\) | |||||||
\(548\) | −1.73536 | − | 5.06339i | −0.0741308 | − | 0.216297i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.331969 | − | 8.32269i | 0.0141552 | − | 0.354881i | ||||
\(551\) | − | 2.13794i | − | 0.0910795i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.1566 | + | 30.1566i | 1.28239 | + | 1.28239i | ||||
\(554\) | −14.7258 | − | 23.6037i | −0.625637 | − | 1.00283i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.1189 | + | 16.2119i | 1.40456 | + | 0.687539i | ||||
\(557\) | 10.9318 | − | 10.9318i | 0.463194 | − | 0.463194i | −0.436507 | − | 0.899701i | \(-0.643785\pi\) |
0.899701 | + | 0.436507i | \(0.143785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.8451i | 1.22002i | ||||||||
\(560\) | 28.7595 | − | 27.0206i | 1.21531 | − | 1.14183i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.44958 | − | 19.2105i | 0.187694 | − | 0.810346i | ||||
\(563\) | −13.9005 | − | 13.9005i | −0.585835 | − | 0.585835i | 0.350666 | − | 0.936501i | \(-0.385955\pi\) |
−0.936501 | + | 0.350666i | \(0.885955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.59205 | + | 27.5316i | 0.109048 | + | 1.15826i | ||||
\(566\) | 24.3543 | − | 15.1940i | 1.02369 | − | 0.638652i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.46401 | + | 9.17690i | −0.313183 | + | 0.385054i | ||||
\(569\) | 3.03632 | 0.127289 | 0.0636446 | − | 0.997973i | \(-0.479728\pi\) | ||||
0.0636446 | + | 0.997973i | \(0.479728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.26119i | − | 0.0527792i | −0.999652 | − | 0.0263896i | \(-0.991599\pi\) | ||
0.999652 | − | 0.0263896i | \(-0.00840105\pi\) | |||||||
\(572\) | 6.77942 | − | 2.32349i | 0.283462 | − | 0.0971498i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.5579 | − | 16.9231i | −0.440678 | − | 0.706357i | ||||
\(575\) | −27.5519 | − | 18.7546i | −1.14899 | − | 0.782119i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.10444 | + | 5.10444i | −0.212501 | + | 0.212501i | −0.805329 | − | 0.592828i | \(-0.798011\pi\) |
0.592828 | + | 0.805329i | \(0.298011\pi\) | |||||||
\(578\) | −4.28736 | + | 18.5101i | −0.178331 | + | 0.769920i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.2006 | + | 27.0259i | 0.506602 | + | 1.12219i | ||||
\(581\) | −3.65081 | −0.151461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.75469 | − | 6.75469i | −0.279751 | − | 0.279751i | ||||
\(584\) | −1.62964 | − | 15.8321i | −0.0674351 | − | 0.655136i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.1459 | + | 21.0715i | 0.543054 | + | 0.870454i | ||||
\(587\) | −2.16591 | + | 2.16591i | −0.0893966 | + | 0.0893966i | −0.750391 | − | 0.660994i | \(-0.770135\pi\) |
0.660994 | + | 0.750391i | \(0.270135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0217916 | 0.000897908 | ||||||||
\(590\) | 16.6564 | + | 21.8350i | 0.685732 | + | 0.898934i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.36823 | − | 42.7091i | 0.220633 | − | 1.75533i | ||||
\(593\) | −14.8495 | + | 14.8495i | −0.609795 | + | 0.609795i | −0.942892 | − | 0.333097i | \(-0.891906\pi\) |
0.333097 | + | 0.942892i | \(0.391906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.8785 | + | 14.3476i | −0.486971 | + | 0.588196i | ||||
\(596\) | −1.09539 | + | 2.23775i | −0.0448690 | + | 0.0916618i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.47080 | − | 27.9368i | 0.264611 | − | 1.14242i | ||||
\(599\) | −20.1979 | −0.825262 | −0.412631 | − | 0.910898i | \(-0.635390\pi\) | ||||
−0.412631 | + | 0.910898i | \(0.635390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9787 | −1.26365 | −0.631823 | − | 0.775113i | \(-0.717693\pi\) | ||||
−0.631823 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(602\) | −13.3504 | + | 57.6388i | −0.544123 | + | 2.34918i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.1042 | + | 14.7362i | 1.22492 | + | 0.599607i | ||||
\(605\) | −13.7071 | + | 16.5563i | −0.557272 | + | 0.673110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.72619 | + | 7.72619i | −0.313596 | + | 0.313596i | −0.846301 | − | 0.532705i | \(-0.821176\pi\) |
0.532705 | + | 0.846301i | \(0.321176\pi\) | |||||||
\(608\) | 0.764941 | + | 1.65587i | 0.0310224 | + | 0.0671545i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0932 | − | 31.5841i | −0.975506 | − | 1.27880i | ||||
\(611\) | −31.5886 | −1.27794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.56398 | − | 7.56398i | 0.305506 | − | 0.305506i | −0.537657 | − | 0.843164i | \(-0.680691\pi\) |
0.843164 | + | 0.537657i | \(0.180691\pi\) | |||||||
\(614\) | 15.8730 | + | 25.4426i | 0.640582 | + | 1.02678i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6221 | − | 1.50510i | 0.589142 | − | 0.0606422i | ||||
\(617\) | −20.1379 | − | 20.1379i | −0.810722 | − | 0.810722i | 0.174020 | − | 0.984742i | \(-0.444324\pi\) |
−0.984742 | + | 0.174020i | \(0.944324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.5448 | 1.06692 | 0.533462 | − | 0.845824i | \(-0.320891\pi\) | ||||
0.533462 | + | 0.845824i | \(0.320891\pi\) | |||||||
\(620\) | −0.275469 | + | 0.124358i | −0.0110631 | + | 0.00499434i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.4451 | − | 45.0956i | 0.418812 | − | 1.80817i | ||||
\(623\) | 1.73869 | − | 1.73869i | 0.0696591 | − | 0.0696591i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2582 | + | 9.16811i | −0.930330 | + | 0.366724i | ||||
\(626\) | −8.73667 | − | 14.0039i | −0.349188 | − | 0.559708i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.33460 | − | 18.4829i | −0.252778 | − | 0.737550i | ||||
\(629\) | 20.3182i | 0.810139i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.2805 | −1.52392 | −0.761961 | − | 0.647623i | \(-0.775763\pi\) | ||||
−0.761961 | + | 0.647623i | \(0.775763\pi\) | |||||||
\(632\) | 17.2517 | − | 21.2108i | 0.686237 | − | 0.843720i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0998 | + | 8.79653i | −0.559976 | + | 0.349355i | ||||
\(635\) | 1.13749 | + | 12.0820i | 0.0451401 | + | 0.479458i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.8128 | + | 26.8128i | 1.06236 | + | 1.06236i | ||||
\(638\) | −2.49238 | + | 10.7605i | −0.0986741 | + | 0.426013i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.1192 | − | 16.5667i | −0.755754 | − | 0.654856i | ||||
\(641\) | 24.4013i | 0.963792i | 0.876228 | + | 0.481896i | \(0.160052\pi\) | ||||
−0.876228 | + | 0.481896i | \(0.839948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.08062 | + | 1.08062i | −0.0426157 | + | 0.0426157i | −0.728094 | − | 0.685478i | \(-0.759593\pi\) |
0.685478 | + | 0.728094i | \(0.259593\pi\) | |||||||
\(644\) | 25.8601 | − | 52.8289i | 1.01903 | − | 2.08175i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.455724 | − | 0.730474i | −0.0179302 | − | 0.0287401i | ||||
\(647\) | −22.0445 | − | 22.0445i | −0.866659 | − | 0.866659i | 0.125442 | − | 0.992101i | \(-0.459965\pi\) |
−0.992101 | + | 0.125442i | \(0.959965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2298i | 0.401556i | ||||||||
\(650\) | −14.5916 | − | 15.8040i | −0.572328 | − | 0.619882i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.2631 | + | 5.57381i | −0.636914 | + | 0.218287i | ||||
\(653\) | 20.9241 | + | 20.9241i | 0.818823 | + | 0.818823i | 0.985937 | − | 0.167115i | \(-0.0534450\pi\) |
−0.167115 | + | 0.985937i | \(0.553445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.64824 | − | 3.19872i | 0.103475 | − | 0.124984i | ||||
\(656\) | −10.0991 | + | 7.84378i | −0.394302 | + | 0.306248i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −63.1209 | − | 14.6202i | −2.46071 | − | 0.569956i | ||||
\(659\) | − | 7.22520i | − | 0.281454i | −0.990048 | − | 0.140727i | \(-0.955056\pi\) | ||
0.990048 | − | 0.140727i | \(-0.0449440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.3836i | − | 0.792830i | −0.918071 | − | 0.396415i | \(-0.870254\pi\) | ||
0.918071 | − | 0.396415i | \(-0.129746\pi\) | |||||||
\(662\) | −2.37240 | + | 10.2425i | −0.0922059 | + | 0.398087i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.239646 | + | 2.32817i | 0.00930006 | + | 0.0903507i | ||||
\(665\) | 0.298171 | + | 3.16704i | 0.0115626 | + | 0.122813i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.2523 | + | 31.2523i | 1.21009 | + | 1.21009i | ||||
\(668\) | −2.58744 | − | 7.54957i | −0.100111 | − | 0.292102i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.32100 | + | 1.11951i | 0.321468 | + | 0.0432505i | ||||
\(671\) | − | 14.7973i | − | 0.571244i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4517 | − | 19.4517i | −0.749807 | − | 0.749807i | 0.224636 | − | 0.974443i | \(-0.427881\pi\) |
−0.974443 | + | 0.224636i | \(0.927881\pi\) | |||||||
\(674\) | 6.59852 | − | 4.11664i | 0.254165 | − | 0.158567i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.29429 | + | 6.72983i | −0.126704 | + | 0.258839i | ||||
\(677\) | 24.8145 | − | 24.8145i | 0.953698 | − | 0.953698i | −0.0452768 | − | 0.998974i | \(-0.514417\pi\) |
0.998974 | + | 0.0452768i | \(0.0144170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65.9957i | 2.53268i | ||||||||
\(680\) | 9.92943 | + | 6.63329i | 0.380776 | + | 0.254375i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.109680 | − | 0.0254042i | −0.00419985 | − | 0.000972779i | ||||
\(683\) | −7.85886 | − | 7.85886i | −0.300711 | − | 0.300711i | 0.540581 | − | 0.841292i | \(-0.318204\pi\) |
−0.841292 | + | 0.540581i | \(0.818204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.95794 | + | 0.560928i | −0.227641 | + | 0.0214320i | ||||
\(686\) | 18.0497 | + | 28.9316i | 0.689139 | + | 1.10461i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 37.6334 | + | 4.73025i | 1.43476 | + | 0.180339i | ||||
\(689\) | −24.6690 | −0.939814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 49.6748i | − | 1.88972i | −0.327479 | − | 0.944858i | \(-0.606199\pi\) | ||
0.327479 | − | 0.944858i | \(-0.393801\pi\) | |||||||
\(692\) | 6.67514 | + | 19.4766i | 0.253751 | + | 0.740389i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.1982 | − | 21.9593i | 1.33611 | − | 0.833563i | ||||
\(695\) | 26.2906 | − | 31.7556i | 0.997260 | − | 1.20456i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.26802 | − | 4.26802i | 0.161663 | − | 0.161663i | ||||
\(698\) | −4.18908 | − | 0.970285i | −0.158559 | − | 0.0367258i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −21.8425 | − | 38.3332i | −0.825570 | − | 1.44886i | ||||
\(701\) | −30.5703 | −1.15462 | −0.577312 | − | 0.816524i | \(-0.695898\pi\) | ||||
−0.577312 | + | 0.816524i | \(0.695898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45360 | + | 2.45360i | 0.0925393 | + | 0.0925393i | ||||
\(704\) | −1.91965 | − | 9.22594i | −0.0723494 | − | 0.347716i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.87941 | − | 3.66801i | 0.221275 | − | 0.138047i | ||||
\(707\) | 29.7269 | − | 29.7269i | 1.11799 | − | 1.11799i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1384 | 0.418310 | 0.209155 | − | 0.977882i | \(-0.432929\pi\) | ||||
0.209155 | + | 0.977882i | \(0.432929\pi\) | |||||||
\(710\) | 8.02125 | + | 10.5151i | 0.301032 | + | 0.394626i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.22292 | − | 0.994655i | −0.0458307 | − | 0.0372763i | ||||
\(713\) | −0.318548 | + | 0.318548i | −0.0119297 | + | 0.0119297i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.751033 | − | 7.97714i | −0.0280870 | − | 0.298328i | ||||
\(716\) | 8.41157 | − | 17.1838i | 0.314355 | − | 0.642188i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.8940 | − | 2.75492i | −0.443880 | − | 0.102813i | ||||
\(719\) | 41.0316 | 1.53022 | 0.765111 | − | 0.643899i | \(-0.222684\pi\) | ||||
0.765111 | + | 0.643899i | \(0.222684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.01359 | −0.0377482 | ||||||||
\(722\) | 26.0338 | + | 6.03001i | 0.968878 | + | 0.224414i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.91169 | − | 7.99110i | 0.145377 | − | 0.296987i | ||||
\(725\) | 32.5696 | − | 6.18758i | 1.20961 | − | 0.229801i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.35975 | + | 4.35975i | −0.161694 | + | 0.161694i | −0.783317 | − | 0.621623i | \(-0.786474\pi\) |
0.621623 | + | 0.783317i | \(0.286474\pi\) | |||||||
\(728\) | 23.9525 | − | 29.4493i | 0.887740 | − | 1.09146i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.6354 | − | 2.37268i | −0.652716 | − | 0.0878168i | ||||
\(731\) | −17.9035 | −0.662185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.3786 | + | 28.3786i | −1.04819 | + | 1.04819i | −0.0494094 | + | 0.998779i | \(0.515734\pi\) |
−0.998779 | + | 0.0494094i | \(0.984266\pi\) | |||||||
\(734\) | −26.1051 | + | 16.2863i | −0.963558 | + | 0.601139i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.3873 | − | 13.0236i | −1.30439 | − | 0.480055i | ||||
\(737\) | 2.21146 | + | 2.21146i | 0.0814603 | + | 0.0814603i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.53862 | 0.240527 | 0.120264 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120264 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(740\) | −45.0180 | − | 17.0141i | −1.65490 | − | 0.625452i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −49.2940 | − | 11.4176i | −1.80964 | − | 0.419153i | ||||
\(743\) | −20.0409 | + | 20.0409i | −0.735230 | + | 0.735230i | −0.971651 | − | 0.236421i | \(-0.924026\pi\) |
0.236421 | + | 0.971651i | \(0.424026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.14563 | + | 1.77638i | 0.0786098 | + | 0.0650816i | ||||
\(746\) | 12.5672 | − | 7.84033i | 0.460117 | − | 0.287055i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.44214 | + | 4.20783i | 0.0527297 | + | 0.153854i | ||||
\(749\) | 73.5974i | 2.68919i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.89337 | 0.288033 | 0.144017 | − | 0.989575i | \(-0.453998\pi\) | ||||
0.144017 | + | 0.989575i | \(0.453998\pi\) | |||||||
\(752\) | −5.18016 | + | 41.2128i | −0.188901 | + | 1.50288i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.0981 | + | 24.2006i | 0.549842 | + | 0.881334i | ||||
\(755\) | 23.8974 | − | 28.8649i | 0.869717 | − | 1.05050i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.76852 | − | 5.76852i | −0.209660 | − | 0.209660i | 0.594463 | − | 0.804123i | \(-0.297365\pi\) |
−0.804123 | + | 0.594463i | \(0.797365\pi\) | |||||||
\(758\) | 9.02352 | + | 2.09005i | 0.327749 | + | 0.0759141i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00009 | − | 0.398038i | 0.0725510 | − | 0.0144384i | ||||
\(761\) | 11.7806i | 0.427045i | 0.976938 | + | 0.213522i | \(0.0684936\pi\) | ||||
−0.976938 | + | 0.213522i | \(0.931506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.8805 | − | 33.8805i | 1.22656 | − | 1.22656i | ||||
\(764\) | −2.78483 | + | 5.68905i | −0.100752 | + | 0.205823i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.2455 | + | 15.7500i | −0.912158 | + | 0.569072i | ||||
\(767\) | 18.6803 | + | 18.6803i | 0.674506 | + | 0.674506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7788i | 1.25416i | 0.778956 | + | 0.627078i | \(0.215749\pi\) | ||||
−0.778956 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(770\) | 2.19135 | − | 16.2877i | 0.0789708 | − | 0.586967i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.987861 | + | 2.88236i | 0.0355539 | + | 0.103738i | ||||
\(773\) | 27.6201 | + | 27.6201i | 0.993426 | + | 0.993426i | 0.999979 | − | 0.00655287i | \(-0.00208586\pi\) |
−0.00655287 | + | 0.999979i | \(0.502086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0630687 | + | 0.331975i | 0.00226549 | + | 0.0119249i | ||||
\(776\) | 42.0864 | − | 4.33208i | 1.51081 | − | 0.155513i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0810921 | + | 0.350105i | −0.00290729 | + | 0.0125519i | ||||
\(779\) | − | 1.03080i | − | 0.0369323i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.92640i | 0.176280i | ||||||||
\(782\) | 17.3398 | + | 4.01628i | 0.620068 | + | 0.143622i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 39.3788 | − | 30.5849i | 1.40639 | − | 1.09232i | ||||
\(785\) | −21.7483 | + | 2.04756i | −0.776232 | + | 0.0730807i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2310 | + | 18.2310i | 0.649864 | + | 0.649864i | 0.952960 | − | 0.303096i | \(-0.0980203\pi\) |
−0.303096 | + | 0.952960i | \(0.598020\pi\) | |||||||
\(788\) | −14.9585 | + | 5.12668i | −0.532875 | + | 0.182631i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.5397 | − | 24.3039i | −0.659613 | − | 0.864694i | ||||
\(791\) | 54.5623i | 1.94001i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.0208 | − | 27.0208i | −0.959537 | − | 0.959537i | ||||
\(794\) | 21.8695 | + | 35.0544i | 0.776120 | + | 1.24403i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.8674 | + | 28.3294i | −0.491518 | + | 1.00411i | ||||
\(797\) | −11.4983 | + | 11.4983i | −0.407290 | + | 0.407290i | −0.880793 | − | 0.473502i | \(-0.842990\pi\) |
0.473502 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.6064i | − | 0.693623i | ||||||
\(800\) | −23.0118 | + | 16.4455i | −0.813591 | + | 0.581438i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.60133 | + | 28.5004i | −0.233101 | + | 1.00638i | ||||
\(803\) | −4.68695 | − | 4.68695i | −0.165399 | − | 0.165399i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.6542 | − | 41.9369i | −1.78533 | − | 1.47808i | ||||
\(806\) | −0.246672 | + | 0.153892i | −0.00868863 | + | 0.00542061i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.9086 | − | 17.0059i | −0.735561 | − | 0.598266i | ||||
\(809\) | −17.8481 | −0.627506 | −0.313753 | − | 0.949505i | \(-0.601586\pi\) | ||||
−0.313753 | + | 0.949505i | \(0.601586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.5242i | 1.45811i | 0.684454 | + | 0.729056i | \(0.260041\pi\) | ||||
−0.684454 | + | 0.729056i | \(0.739959\pi\) | |||||||
\(812\) | 18.9685 | + | 55.3460i | 0.665665 | + | 1.94226i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.48887 | − | 15.2096i | −0.332585 | − | 0.533096i | ||||
\(815\) | 1.80165 | + | 19.1364i | 0.0631091 | + | 0.670317i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16201 | + | 2.16201i | −0.0756390 | + | 0.0756390i | ||||
\(818\) | −8.60931 | + | 37.1696i | −0.301017 | + | 1.29960i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.88247 | + | 13.0304i | 0.205425 | + | 0.455042i | ||||
\(821\) | −28.9849 | −1.01158 | −0.505790 | − | 0.862657i | \(-0.668799\pi\) | ||||
−0.505790 | + | 0.862657i | \(0.668799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6586 | + | 20.6586i | 0.720112 | + | 0.720112i | 0.968628 | − | 0.248516i | \(-0.0799428\pi\) |
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(824\) | 0.0665341 | + | 0.646383i | 0.00231783 | + | 0.0225178i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.6814 | + | 45.9731i | 0.997955 | + | 1.59961i | ||||
\(827\) | 25.4075 | − | 25.4075i | 0.883504 | − | 0.883504i | −0.110385 | − | 0.993889i | \(-0.535208\pi\) |
0.993889 | + | 0.110385i | \(0.0352082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.7882 | −0.860931 | −0.430465 | − | 0.902607i | \(-0.641651\pi\) | ||||
−0.430465 | + | 0.902607i | \(0.641651\pi\) | |||||||
\(830\) | 2.59336 | + | 0.348913i | 0.0900170 | + | 0.0121109i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.3525 | − | 13.3418i | −0.705598 | − | 0.462542i | ||||
\(833\) | −16.6421 | + | 16.6421i | −0.576614 | + | 0.576614i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.88336 | + | 0.836351i | −0.307421 | + | 0.0289431i | ||||
\(836\) | 0.682283 | + | 0.333982i | 0.0235973 | + | 0.0115510i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.9705 | + | 47.3636i | −0.378969 | + | 1.63615i | ||||
\(839\) | 52.8553 | 1.82477 | 0.912383 | − | 0.409338i | \(-0.134240\pi\) | ||||
0.912383 | + | 0.409338i | \(0.134240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9627 | −0.515954 | ||||||||
\(842\) | 1.29488 | − | 5.59050i | 0.0446247 | − | 0.192661i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.60864 | + | 19.6292i | −0.330743 | + | 0.675666i | ||||
\(845\) | 6.45279 | + | 5.34230i | 0.221983 | + | 0.183781i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.9881 | + | 29.9881i | −1.03040 | + | 1.03040i | ||||
\(848\) | −4.04542 | + | 32.1850i | −0.138920 | + | 1.10524i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.80916 | − | 9.05665i | 0.336451 | − | 0.310641i | ||||
\(851\) | −71.7331 | −2.45898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.39491 | + | 7.39491i | −0.253197 | + | 0.253197i | −0.822280 | − | 0.569083i | \(-0.807298\pi\) |
0.569083 | + | 0.822280i | \(0.307298\pi\) | |||||||
\(854\) | −41.4873 | − | 66.4995i | −1.41967 | − | 2.27557i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46.9341 | − | 4.83107i | 1.60418 | − | 0.165123i | ||||
\(857\) | 6.82308 | + | 6.82308i | 0.233072 | + | 0.233072i | 0.813974 | − | 0.580902i | \(-0.197300\pi\) |
−0.580902 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.6736 | 1.49012 | 0.745061 | − | 0.666996i | \(-0.232420\pi\) | ||||
0.745061 | + | 0.666996i | \(0.232420\pi\) | |||||||
\(860\) | 14.9921 | − | 39.6679i | 0.511227 | − | 1.35267i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.13306 | + | 22.1613i | −0.174833 | + | 0.754817i | ||||
\(863\) | 13.1338 | − | 13.1338i | 0.447080 | − | 0.447080i | −0.447303 | − | 0.894383i | \(-0.647615\pi\) |
0.894383 | + | 0.447303i | \(0.147615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.9175 | − | 2.15764i | 0.779219 | − | 0.0733620i | ||||
\(866\) | 3.22681 | + | 5.17221i | 0.109651 | + | 0.175759i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.564129 | + | 0.193342i | −0.0191478 | + | 0.00656246i | ||||
\(869\) | − | 11.3865i | − | 0.386261i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.07654 | 0.273663 | ||||||||
\(872\) | −23.8301 | − | 19.3821i | −0.806987 | − | 0.656361i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.57893 | − | 1.60893i | 0.0872336 | − | 0.0544228i | ||||
\(875\) | −47.3840 | + | 13.7083i | −1.60187 | + | 0.463426i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.9437 | + | 28.9437i | 0.977360 | + | 0.977360i | 0.999749 | − | 0.0223891i | \(-0.00712727\pi\) |
−0.0223891 | + | 0.999749i | \(0.507127\pi\) | |||||||
\(878\) | −1.52687 | + | 6.59207i | −0.0515294 | + | 0.222472i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.5307 | − | 0.328304i | −0.354990 | − | 0.0110671i | ||||
\(881\) | − | 7.23302i | − | 0.243687i | −0.992549 | − | 0.121843i | \(-0.961119\pi\) | ||
0.992549 | − | 0.121843i | \(-0.0388805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.01625 | + | 7.01625i | −0.236116 | + | 0.236116i | −0.815239 | − | 0.579124i | \(-0.803395\pi\) |
0.579124 | + | 0.815239i | \(0.303395\pi\) | |||||||
\(884\) | 10.3172 | + | 5.05033i | 0.347005 | + | 0.169861i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.9210 | + | 19.1080i | 0.400494 | + | 0.641946i | ||||
\(887\) | −15.2597 | − | 15.2597i | −0.512371 | − | 0.512371i | 0.402881 | − | 0.915252i | \(-0.368009\pi\) |
−0.915252 | + | 0.402881i | \(0.868009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.9441i | 0.803061i | ||||||||
\(890\) | −1.40125 | + | 1.06891i | −0.0469700 | + | 0.0358301i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.869206 | + | 2.53615i | 0.0291032 | + | 0.0849166i | ||||
\(893\) | −2.36764 | − | 2.36764i | −0.0792301 | − | 0.0792301i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4764 | − | 13.6409i | −0.550745 | − | 0.455965i | ||||
\(896\) | −34.4938 | − | 36.0795i | −1.15236 | − | 1.20533i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.3211 | + | 2.39060i | 0.344420 | + | 0.0797753i | ||||
\(899\) | − | 0.448102i | − | 0.0149450i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.3115i | − | 0.510100i | ||||||
\(902\) | −1.20169 | + | 5.18813i | −0.0400119 | + | 0.172746i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.7952 | − | 3.58157i | 1.15727 | − | 0.119121i | ||||
\(905\) | −7.66214 | − | 6.34353i | −0.254698 | − | 0.210866i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.0510 | − | 36.0510i | −1.19706 | − | 1.19706i | −0.975044 | − | 0.222011i | \(-0.928738\pi\) |
−0.222011 | − | 0.975044i | \(-0.571262\pi\) | |||||||
\(908\) | 13.0414 | − | 4.46963i | 0.432793 | − | 0.148330i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −25.7408 | − | 33.7438i | −0.853298 | − | 1.11860i | ||||
\(911\) | − | 24.0944i | − | 0.798282i | −0.916890 | − | 0.399141i | \(-0.869308\pi\) | ||
0.916890 | − | 0.399141i | \(-0.130692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.689236 | + | 0.689236i | 0.0228104 | + | 0.0228104i | ||||
\(914\) | 24.1289 | − | 15.0534i | 0.798113 | − | 0.497922i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.8501 | + | 15.1013i | 1.01932 | + | 0.498963i | ||||
\(917\) | 5.79377 | − | 5.79377i | 0.191327 | − | 0.191327i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 47.1031i | − | 1.55379i | −0.629632 | − | 0.776893i | \(-0.716794\pi\) | ||
0.629632 | − | 0.776893i | \(-0.283206\pi\) | |||||||
\(920\) | −23.4187 | + | 35.0557i | −0.772093 | + | 1.15575i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.7786 | − | 6.20253i | −0.881906 | − | 0.204269i | ||||
\(923\) | 8.99592 | + | 8.99592i | 0.296104 | + | 0.296104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.2772 | + | 44.4795i | −0.995508 | + | 1.46248i | ||||
\(926\) | 2.31616 | + | 3.71254i | 0.0761137 | + | 0.122002i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 34.0498 | − | 15.7295i | 1.11774 | − | 0.516347i | ||||
\(929\) | 34.0301 | 1.11649 | 0.558246 | − | 0.829675i | \(-0.311474\pi\) | ||||
0.558246 | + | 0.829675i | \(0.311474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.01936i | 0.131729i | ||||||||
\(932\) | 45.9398 | − | 15.7448i | 1.50481 | − | 0.515738i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.51235 | + | 2.19127i | −0.114928 | + | 0.0717004i | ||||
\(935\) | 4.95123 | − | 0.466149i | 0.161923 | − | 0.0152447i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9441 | − | 26.9441i | 0.880227 | − | 0.880227i | −0.113330 | − | 0.993557i | \(-0.536152\pi\) |
0.993557 | + | 0.113330i | \(0.0361519\pi\) | |||||||
\(938\) | 16.1387 | + | 3.73808i | 0.526947 | + | 0.122053i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 43.4409 | + | 16.4181i | 1.41689 | + | 0.535498i | ||||
\(941\) | −19.1115 | −0.623018 | −0.311509 | − | 0.950243i | \(-0.600834\pi\) | ||||
−0.311509 | + | 0.950243i | \(0.600834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0682 | + | 15.0682i | 0.490687 | + | 0.490687i | ||||
\(944\) | 27.4350 | − | 21.3083i | 0.892934 | − | 0.693527i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.4020 | − | 8.36118i | 0.435738 | − | 0.271846i | ||||
\(947\) | 26.6896 | − | 26.6896i | 0.867294 | − | 0.867294i | −0.124878 | − | 0.992172i | \(-0.539854\pi\) |
0.992172 | + | 0.124878i | \(0.0398540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1173 | −0.555652 | ||||||||
\(950\) | 0.0908715 | − | 2.27821i | 0.00294826 | − | 0.0739150i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.2785 | + | 14.8668i | 0.592411 | + | 0.481835i | ||||
\(953\) | −18.0251 | + | 18.0251i | −0.583890 | + | 0.583890i | −0.935970 | − | 0.352080i | \(-0.885475\pi\) |
0.352080 | + | 0.935970i | \(0.385475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.45486 | + | 4.51611i | 0.176515 | + | 0.146138i | ||||
\(956\) | −35.6297 | − | 17.4410i | −1.15235 | − | 0.564082i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.9541 | + | 8.79103i | 1.22624 | + | 0.284025i | ||||
\(959\) | −11.8075 | −0.381284 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9954 | −0.999853 | ||||||||
\(962\) | −45.1010 | − | 10.4464i | −1.45411 | − | 0.336805i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.20244 | − | 2.54663i | −0.167559 | − | 0.0820214i | ||||
\(965\) | 3.39159 | − | 0.319311i | 0.109179 | − | 0.0102790i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9523 | − | 20.9523i | 0.673779 | − | 0.673779i | −0.284806 | − | 0.958585i | \(-0.591929\pi\) |
0.958585 | + | 0.284806i | \(0.0919291\pi\) | |||||||
\(968\) | 21.0923 | + | 17.1554i | 0.677933 | + | 0.551395i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.30730 | − | 46.8803i | 0.202515 | − | 1.50523i | ||||
\(971\) | −6.93592 | −0.222584 | −0.111292 | − | 0.993788i | \(-0.535499\pi\) | ||||
−0.111292 | + | 0.993788i | \(0.535499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.5182 | − | 57.5182i | 1.84395 | − | 1.84395i | ||||
\(974\) | −47.0599 | + | 29.3594i | −1.50789 | + | 0.940737i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.6844 | + | 30.8222i | −1.27027 | + | 0.986595i | ||||
\(977\) | 6.98111 | + | 6.98111i | 0.223346 | + | 0.223346i | 0.809906 | − | 0.586560i | \(-0.199518\pi\) |
−0.586560 | + | 0.809906i | \(0.699518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.656493 | −0.0209816 | ||||||||
\(980\) | −22.9372 | − | 50.8089i | −0.732703 | − | 1.62303i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.56392 | + | 0.825484i | 0.113729 | + | 0.0263422i | ||||
\(983\) | −21.0079 | + | 21.0079i | −0.670047 | + | 0.670047i | −0.957727 | − | 0.287680i | \(-0.907116\pi\) |
0.287680 | + | 0.957727i | \(0.407116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65712 | + | 17.6013i | 0.0528004 | + | 0.560823i | ||||
\(986\) | −15.0208 | + | 9.37107i | −0.478359 | + | 0.298436i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.85576 | − | 0.636020i | 0.0590397 | − | 0.0202345i | ||||
\(989\) | − | 63.2081i | − | 2.00990i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.65846 | 0.211513 | 0.105756 | − | 0.994392i | \(-0.466274\pi\) | ||||
0.105756 | + | 0.994392i | \(0.466274\pi\) | |||||||
\(992\) | 0.160328 | + | 0.347062i | 0.00509040 | + | 0.0110192i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.8122 | + | 22.1394i | 0.438096 | + | 0.702219i | ||||
\(995\) | 27.1632 | + | 22.4886i | 0.861132 | + | 0.712936i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.19447 | − | 9.19447i | −0.291192 | − | 0.291192i | 0.546359 | − | 0.837551i | \(-0.316013\pi\) |
−0.837551 | + | 0.546359i | \(0.816013\pi\) | |||||||
\(998\) | 35.2634 | + | 8.16779i | 1.11624 | + | 0.258547i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 360.2.x.a.53.2 | ✓ | 48 | |
3.2 | odd | 2 | inner | 360.2.x.a.53.23 | yes | 48 | |
4.3 | odd | 2 | 1440.2.bj.a.593.17 | 48 | |||
5.2 | odd | 4 | inner | 360.2.x.a.197.14 | yes | 48 | |
8.3 | odd | 2 | 1440.2.bj.a.593.7 | 48 | |||
8.5 | even | 2 | inner | 360.2.x.a.53.11 | yes | 48 | |
12.11 | even | 2 | 1440.2.bj.a.593.8 | 48 | |||
15.2 | even | 4 | inner | 360.2.x.a.197.11 | yes | 48 | |
20.7 | even | 4 | 1440.2.bj.a.17.18 | 48 | |||
24.5 | odd | 2 | inner | 360.2.x.a.53.14 | yes | 48 | |
24.11 | even | 2 | 1440.2.bj.a.593.18 | 48 | |||
40.27 | even | 4 | 1440.2.bj.a.17.8 | 48 | |||
40.37 | odd | 4 | inner | 360.2.x.a.197.23 | yes | 48 | |
60.47 | odd | 4 | 1440.2.bj.a.17.7 | 48 | |||
120.77 | even | 4 | inner | 360.2.x.a.197.2 | yes | 48 | |
120.107 | odd | 4 | 1440.2.bj.a.17.17 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.2 | ✓ | 48 | 1.1 | even | 1 | trivial | |
360.2.x.a.53.11 | yes | 48 | 8.5 | even | 2 | inner | |
360.2.x.a.53.14 | yes | 48 | 24.5 | odd | 2 | inner | |
360.2.x.a.53.23 | yes | 48 | 3.2 | odd | 2 | inner | |
360.2.x.a.197.2 | yes | 48 | 120.77 | even | 4 | inner | |
360.2.x.a.197.11 | yes | 48 | 15.2 | even | 4 | inner | |
360.2.x.a.197.14 | yes | 48 | 5.2 | odd | 4 | inner | |
360.2.x.a.197.23 | yes | 48 | 40.37 | odd | 4 | inner | |
1440.2.bj.a.17.7 | 48 | 60.47 | odd | 4 | |||
1440.2.bj.a.17.8 | 48 | 40.27 | even | 4 | |||
1440.2.bj.a.17.17 | 48 | 120.107 | odd | 4 | |||
1440.2.bj.a.17.18 | 48 | 20.7 | even | 4 | |||
1440.2.bj.a.593.7 | 48 | 8.3 | odd | 2 | |||
1440.2.bj.a.593.8 | 48 | 12.11 | even | 2 | |||
1440.2.bj.a.593.17 | 48 | 4.3 | odd | 2 | |||
1440.2.bj.a.593.18 | 48 | 24.11 | even | 2 |