Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(207,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.207");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.s (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 207.4 | ||
Character | \(\chi\) | \(=\) | 1600.207 |
Dual form | 1600.2.s.e.943.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.86755 | −1.07823 | −0.539115 | − | 0.842232i | \(-0.681241\pi\) | ||||
−0.539115 | + | 0.842232i | \(0.681241\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.719989 | + | 0.719989i | 0.272130 | + | 0.272130i | 0.829957 | − | 0.557827i | \(-0.188365\pi\) |
−0.557827 | + | 0.829957i | \(0.688365\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.487737 | 0.162579 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.805654 | − | 0.805654i | 0.242914 | − | 0.242914i | −0.575141 | − | 0.818055i | \(-0.695053\pi\) |
0.818055 | + | 0.575141i | \(0.195053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.90473i | 1.63768i | 0.574023 | + | 0.818839i | \(0.305382\pi\) | ||||
−0.574023 | + | 0.818839i | \(0.694618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.17145 | − | 5.17145i | −1.25426 | − | 1.25426i | −0.953792 | − | 0.300469i | \(-0.902857\pi\) |
−0.300469 | − | 0.953792i | \(-0.597143\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.16370 | − | 1.16370i | 0.266971 | − | 0.266971i | −0.560908 | − | 0.827878i | \(-0.689548\pi\) |
0.827878 | + | 0.560908i | \(0.189548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34461 | − | 1.34461i | −0.293419 | − | 0.293419i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.30177 | + | 2.30177i | −0.479953 | + | 0.479953i | −0.905116 | − | 0.425164i | \(-0.860217\pi\) |
0.425164 | + | 0.905116i | \(0.360217\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.69177 | 0.902932 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.71953 | + | 3.71953i | 0.690699 | + | 0.690699i | 0.962386 | − | 0.271687i | \(-0.0875814\pi\) |
−0.271687 | + | 0.962386i | \(0.587581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.82775i | − | 1.76512i | −0.470204 | − | 0.882558i | \(-0.655820\pi\) | ||
0.470204 | − | 0.882558i | \(-0.344180\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50460 | + | 1.50460i | −0.261917 | + | 0.261917i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.71983i | − | 0.282739i | −0.989957 | − | 0.141369i | \(-0.954850\pi\) | ||
0.989957 | − | 0.141369i | \(-0.0451505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 11.0274i | − | 1.76579i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.93637i | 0.614758i | 0.951587 | + | 0.307379i | \(0.0994519\pi\) | ||||
−0.951587 | + | 0.307379i | \(0.900548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.82362i | 1.34559i | 0.739829 | + | 0.672794i | \(0.234906\pi\) | ||||
−0.739829 | + | 0.672794i | \(0.765094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.21130 | + | 3.21130i | −0.468417 | + | 0.468417i | −0.901401 | − | 0.432985i | \(-0.857460\pi\) |
0.432985 | + | 0.901401i | \(0.357460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.96323i | − | 0.851890i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.65793 | + | 9.65793i | 1.35238 | + | 1.35238i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.60748 | −1.18233 | −0.591164 | − | 0.806551i | \(-0.701332\pi\) | ||||
−0.591164 | + | 0.806551i | \(0.701332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.17326 | + | 2.17326i | −0.287856 | + | 0.287856i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.24522 | − | 5.24522i | −0.682870 | − | 0.682870i | 0.277776 | − | 0.960646i | \(-0.410403\pi\) |
−0.960646 | + | 0.277776i | \(0.910403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.59176 | − | 1.59176i | 0.203804 | − | 0.203804i | −0.597824 | − | 0.801628i | \(-0.703968\pi\) |
0.801628 | + | 0.597824i | \(0.203968\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.351165 | + | 0.351165i | 0.0442426 | + | 0.0442426i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.29532i | − | 1.13560i | −0.823165 | − | 0.567802i | \(-0.807794\pi\) | ||
0.823165 | − | 0.567802i | \(-0.192206\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.29867 | − | 4.29867i | 0.517499 | − | 0.517499i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.33581 | −1.10796 | −0.553979 | − | 0.832531i | \(-0.686891\pi\) | ||||
−0.553979 | + | 0.832531i | \(0.686891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.57821 | − | 8.57821i | −1.00400 | − | 1.00400i | −0.999992 | − | 0.00401200i | \(-0.998723\pi\) |
−0.00401200 | − | 0.999992i | \(-0.501277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.16012 | 0.132208 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.70231 | 0.191525 | 0.0957625 | − | 0.995404i | \(-0.469471\pi\) | ||||
0.0957625 | + | 0.995404i | \(0.469471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.2253 | −1.13615 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8974 | −1.52544 | −0.762718 | − | 0.646732i | \(-0.776135\pi\) | ||||
−0.762718 | + | 0.646732i | \(0.776135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.94640 | − | 6.94640i | −0.744732 | − | 0.744732i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.48540 | −0.475452 | −0.237726 | − | 0.971332i | \(-0.576402\pi\) | ||||
−0.237726 | + | 0.971332i | \(0.576402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.25134 | + | 4.25134i | −0.445662 | + | 0.445662i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.3538i | 1.90320i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.46476 | − | 4.46476i | −0.453327 | − | 0.453327i | 0.443130 | − | 0.896457i | \(-0.353868\pi\) |
−0.896457 | + | 0.443130i | \(0.853868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.392947 | − | 0.392947i | 0.0394927 | − | 0.0394927i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.04273 | − | 9.04273i | −0.899785 | − | 0.899785i | 0.0956319 | − | 0.995417i | \(-0.469513\pi\) |
−0.995417 | + | 0.0956319i | \(0.969513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.89360 | − | 8.89360i | 0.876312 | − | 0.876312i | −0.116839 | − | 0.993151i | \(-0.537276\pi\) |
0.993151 | + | 0.116839i | \(0.0372760\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.29532 | −0.898612 | −0.449306 | − | 0.893378i | \(-0.648329\pi\) | ||||
−0.449306 | + | 0.893378i | \(0.648329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.10635 | − | 4.10635i | −0.393317 | − | 0.393317i | 0.482551 | − | 0.875868i | \(-0.339710\pi\) |
−0.875868 | + | 0.482551i | \(0.839710\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.21187i | 0.304857i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.51147 | − | 7.51147i | 0.706619 | − | 0.706619i | −0.259203 | − | 0.965823i | \(-0.583460\pi\) |
0.965823 | + | 0.259203i | \(0.0834600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.87996i | 0.266252i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.44677i | − | 0.682644i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.70184i | 0.881986i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.35136i | − | 0.662850i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.66639 | − | 7.66639i | 0.680282 | − | 0.680282i | −0.279782 | − | 0.960064i | \(-0.590262\pi\) |
0.960064 | + | 0.279782i | \(0.0902621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 16.4785i | − | 1.45085i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70610 | + | 1.70610i | 0.149062 | + | 0.149062i | 0.777699 | − | 0.628637i | \(-0.216387\pi\) |
−0.628637 | + | 0.777699i | \(0.716387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.67570 | 0.145302 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.69414 | + | 1.69414i | −0.144740 | + | 0.144740i | −0.775764 | − | 0.631024i | \(-0.782635\pi\) |
0.631024 | + | 0.775764i | \(0.282635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.38206 | + | 2.38206i | 0.202044 | + | 0.202044i | 0.800875 | − | 0.598831i | \(-0.204368\pi\) |
−0.598831 | + | 0.800875i | \(0.704368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.99726 | − | 5.99726i | 0.505061 | − | 0.505061i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.75717 | + | 4.75717i | 0.397815 | + | 0.397815i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.1366i | 0.918533i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.49691 | − | 2.49691i | 0.204555 | − | 0.204555i | −0.597393 | − | 0.801948i | \(-0.703797\pi\) |
0.801948 | + | 0.597393i | \(0.203797\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5505 | −1.34686 | −0.673431 | − | 0.739250i | \(-0.735180\pi\) | ||||
−0.673431 | + | 0.739250i | \(0.735180\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.52231 | − | 2.52231i | −0.203916 | − | 0.203916i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.07087 | 0.404699 | 0.202350 | − | 0.979313i | \(-0.435142\pi\) | ||||
0.202350 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.0749 | 1.27482 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.31450 | −0.261219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.3065 | −1.19890 | −0.599450 | − | 0.800412i | \(-0.704614\pi\) | ||||
−0.599450 | + | 0.800412i | \(0.704614\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.78800 | − | 4.78800i | −0.370506 | − | 0.370506i | 0.497155 | − | 0.867662i | \(-0.334378\pi\) |
−0.867662 | + | 0.497155i | \(0.834378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.8659 | −1.68199 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.567579 | − | 0.567579i | 0.0434038 | − | 0.0434038i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.32156i | − | 0.708705i | −0.935112 | − | 0.354353i | \(-0.884701\pi\) | ||
0.935112 | − | 0.354353i | \(-0.115299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.79570 | + | 9.79570i | 0.736290 | + | 0.736290i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6273 | + | 15.6273i | −1.16804 | + | 1.16804i | −0.185369 | + | 0.982669i | \(0.559348\pi\) |
−0.982669 | + | 0.185369i | \(0.940652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0056 | + | 17.0056i | 1.26401 | + | 1.26401i | 0.949131 | + | 0.314882i | \(0.101965\pi\) |
0.314882 | + | 0.949131i | \(0.398035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.97268 | + | 2.97268i | −0.219747 | + | 0.219747i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.33280 | −0.609355 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.37802 | + | 3.37802i | 0.245715 | + | 0.245715i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.88531i | − | 0.281131i | −0.990071 | − | 0.140566i | \(-0.955108\pi\) | ||
0.990071 | − | 0.140566i | \(-0.0448921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.68299 | + | 3.68299i | −0.265108 | + | 0.265108i | −0.827125 | − | 0.562018i | \(-0.810025\pi\) |
0.562018 | + | 0.827125i | \(0.310025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.2901i | − | 0.875633i | −0.899064 | − | 0.437816i | \(-0.855752\pi\) | ||
0.899064 | − | 0.437816i | \(-0.144248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6548i | 0.897075i | 0.893764 | + | 0.448537i | \(0.148055\pi\) | ||||
−0.893764 | + | 0.448537i | \(0.851945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.3595i | 1.22444i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.35604i | 0.375920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.12266 | + | 1.12266i | −0.0780302 | + | 0.0780302i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.87508i | − | 0.129702i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.57346 | − | 2.57346i | −0.177164 | − | 0.177164i | 0.612954 | − | 0.790118i | \(-0.289981\pi\) |
−0.790118 | + | 0.612954i | \(0.789981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.4351 | 1.19463 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.07587 | − | 7.07587i | 0.480341 | − | 0.480341i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0202 | + | 16.0202i | 1.08255 | + | 1.08255i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.5360 | − | 30.5360i | 2.05407 | − | 2.05407i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.55375 | + | 9.55375i | 0.639766 | + | 0.639766i | 0.950498 | − | 0.310731i | \(-0.100574\pi\) |
−0.310731 | + | 0.950498i | \(0.600574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8481i | 0.852759i | 0.904544 | + | 0.426380i | \(0.140211\pi\) | ||||
−0.904544 | + | 0.426380i | \(0.859789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.96090 | − | 1.96090i | 0.129580 | − | 0.129580i | −0.639342 | − | 0.768922i | \(-0.720793\pi\) |
0.768922 | + | 0.639342i | \(0.220793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.16659 | −0.142551 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.39089 | − | 7.39089i | −0.484193 | − | 0.484193i | 0.422275 | − | 0.906468i | \(-0.361232\pi\) |
−0.906468 | + | 0.422275i | \(0.861232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.17915 | −0.206508 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.7765 | −0.697074 | −0.348537 | − | 0.937295i | \(-0.613321\pi\) | ||||
−0.348537 | + | 0.937295i | \(0.613321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5670 | −0.938344 | −0.469172 | − | 0.883107i | \(-0.655448\pi\) | ||||
−0.469172 | + | 0.883107i | \(0.655448\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.02097 | 0.322095 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.87133 | + | 6.87133i | 0.437212 | + | 0.437212i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.9540 | 1.64477 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1001 | − | 12.1001i | 0.763750 | − | 0.763750i | −0.213248 | − | 0.976998i | \(-0.568404\pi\) |
0.976998 | + | 0.213248i | \(0.0684043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.70887i | 0.233174i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6083 | + | 17.6083i | 1.09838 | + | 1.09838i | 0.994601 | + | 0.103775i | \(0.0330922\pi\) |
0.103775 | + | 0.994601i | \(0.466908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.23826 | − | 1.23826i | 0.0769417 | − | 0.0769417i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.81415 | + | 1.81415i | 0.112293 | + | 0.112293i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1083 | − | 12.1083i | 0.746630 | − | 0.746630i | −0.227214 | − | 0.973845i | \(-0.572962\pi\) |
0.973845 | + | 0.227214i | \(0.0729618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.37671 | 0.512646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.20149 | + | 6.20149i | 0.378112 | + | 0.378112i | 0.870421 | − | 0.492309i | \(-0.163847\pi\) |
−0.492309 | + | 0.870421i | \(0.663847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.11166i | − | 0.310511i | −0.987874 | − | 0.155256i | \(-0.950380\pi\) | ||
0.987874 | − | 0.155256i | \(-0.0496201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.93959 | − | 7.93959i | 0.480526 | − | 0.480526i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.65720i | 0.279824i | 0.990164 | + | 0.139912i | \(0.0446820\pi\) | ||||
−0.990164 | + | 0.139912i | \(0.955318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.79335i | − | 0.286971i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 26.7402i | − | 1.59519i | −0.603194 | − | 0.797595i | \(-0.706105\pi\) | ||
0.603194 | − | 0.797595i | \(-0.293895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.12034i | − | 0.126041i | −0.998012 | − | 0.0630205i | \(-0.979927\pi\) | ||
0.998012 | − | 0.0630205i | \(-0.0200733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.83414 | + | 2.83414i | −0.167294 | + | 0.167294i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.4877i | 2.14634i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.33815 | + | 8.33815i | 0.488791 | + | 0.488791i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7244 | 0.918632 | 0.459316 | − | 0.888273i | \(-0.348095\pi\) | ||||
0.459316 | + | 0.888273i | \(0.348095\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.77995 | − | 3.77995i | 0.219335 | − | 0.219335i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.5914 | − | 13.5914i | −0.786008 | − | 0.786008i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.35291 | + | 6.35291i | −0.366175 | + | 0.366175i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.8877 | + | 16.8877i | 0.970175 | + | 0.970175i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.32655i | 0.304002i | 0.988380 | + | 0.152001i | \(0.0485717\pi\) | ||||
−0.988380 | + | 0.152001i | \(0.951428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.6092 | + | 16.6092i | −0.944866 | + | 0.944866i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8269 | 0.897459 | 0.448730 | − | 0.893668i | \(-0.351877\pi\) | ||||
0.448730 | + | 0.893668i | \(0.351877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4637 | + | 14.4637i | 0.817539 | + | 0.817539i | 0.985751 | − | 0.168212i | \(-0.0537993\pi\) |
−0.168212 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.38384 | −0.302387 | −0.151193 | − | 0.988504i | \(-0.548312\pi\) | ||||
−0.151193 | + | 0.988504i | \(0.548312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.99331 | 0.335561 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3595 | 0.968910 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0360 | −0.669702 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.66882 | + | 7.66882i | 0.424086 | + | 0.424086i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.62420 | −0.254941 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.04895 | − | 5.04895i | 0.277516 | − | 0.277516i | −0.554601 | − | 0.832116i | \(-0.687129\pi\) |
0.832116 | + | 0.554601i | \(0.187129\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.838825i | − | 0.0459673i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.10233 | − | 8.10233i | −0.441362 | − | 0.441362i | 0.451107 | − | 0.892470i | \(-0.351029\pi\) |
−0.892470 | + | 0.451107i | \(0.851029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0280 | + | 14.0280i | −0.761898 | + | 0.761898i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.91777 | − | 7.91777i | −0.428771 | − | 0.428771i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.33338 | − | 9.33338i | 0.503955 | − | 0.503955i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.87019 | 0.422494 | 0.211247 | − | 0.977433i | \(-0.432248\pi\) | ||||
0.211247 | + | 0.977433i | \(0.432248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.7492 | + | 18.7492i | 1.00362 | + | 1.00362i | 0.999993 | + | 0.00363019i | \(0.00115553\pi\) |
0.00363019 | + | 0.999993i | \(0.498844\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.7037i | 1.47871i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.0830593 | − | 0.0830593i | 0.00442080 | − | 0.00442080i | −0.704893 | − | 0.709314i | \(-0.749005\pi\) |
0.709314 | + | 0.704893i | \(0.249005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9072i | 0.736047i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.9409i | 1.89689i | 0.316941 | + | 0.948445i | \(0.397344\pi\) | ||||
−0.316941 | + | 0.948445i | \(0.602656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2916i | 0.857453i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 18.1187i | − | 0.950983i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.6922 | − | 23.6922i | 1.23672 | − | 1.23672i | 0.275389 | − | 0.961333i | \(-0.411193\pi\) |
0.961333 | − | 0.275389i | \(-0.0888066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.91991i | 0.0999467i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.19729 | − | 6.19729i | −0.321747 | − | 0.321747i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.8655 | −1.44282 | −0.721410 | − | 0.692508i | \(-0.756506\pi\) | ||||
−0.721410 | + | 0.692508i | \(0.756506\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.9628 | + | 21.9628i | −1.13114 | + | 1.13114i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4005 | + | 18.4005i | 0.945168 | + | 0.945168i | 0.998573 | − | 0.0534045i | \(-0.0170073\pi\) |
−0.0534045 | + | 0.998573i | \(0.517007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3173 | + | 14.3173i | −0.733500 | + | 0.733500i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3966 | − | 27.3966i | −1.39990 | − | 1.39990i | −0.800298 | − | 0.599603i | \(-0.795325\pi\) |
−0.599603 | − | 0.800298i | \(-0.704675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.30360i | 0.218764i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.05190 | + | 9.05190i | −0.458950 | + | 0.458950i | −0.898311 | − | 0.439361i | \(-0.855205\pi\) |
0.439361 | + | 0.898311i | \(0.355205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.8070 | 1.20397 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.18622 | − | 3.18622i | −0.160724 | − | 0.160724i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6052 | 0.582448 | 0.291224 | − | 0.956655i | \(-0.405937\pi\) | ||||
0.291224 | + | 0.956655i | \(0.405937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.12945 | −0.156668 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.94759 | −0.496759 | −0.248379 | − | 0.968663i | \(-0.579898\pi\) | ||||
−0.248379 | + | 0.968663i | \(0.579898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 58.0302 | 2.89069 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.38559 | − | 1.38559i | −0.0686811 | − | 0.0686811i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.7129 | −1.22198 | −0.610988 | − | 0.791640i | \(-0.709228\pi\) | ||||
−0.610988 | + | 0.791640i | \(0.709228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.16389 | − | 3.16389i | 0.156063 | − | 0.156063i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 7.55300i | − | 0.371659i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.44861 | − | 4.44861i | −0.217849 | − | 0.217849i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9537 | − | 12.9537i | 0.632829 | − | 0.632829i | −0.315947 | − | 0.948777i | \(-0.602322\pi\) |
0.948777 | + | 0.315947i | \(0.102322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.99009 | − | 8.99009i | −0.438150 | − | 0.438150i | 0.453239 | − | 0.891389i | \(-0.350268\pi\) |
−0.891389 | + | 0.453239i | \(0.850268\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.56627 | + | 1.56627i | −0.0761547 | + | 0.0761547i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.29210 | 0.110922 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.88425 | − | 8.88425i | −0.428936 | − | 0.428936i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.8177i | − | 1.00275i | −0.865230 | − | 0.501376i | \(-0.832828\pi\) | ||
0.865230 | − | 0.501376i | \(-0.167172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.70002 | − | 7.70002i | 0.370039 | − | 0.370039i | −0.497452 | − | 0.867491i | \(-0.665731\pi\) |
0.867491 | + | 0.497452i | \(0.165731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.35714i | 0.256267i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.4535i | − | 1.83529i | −0.397407 | − | 0.917643i | \(-0.630090\pi\) | ||
0.397407 | − | 0.917643i | \(-0.369910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.90849i | − | 0.138499i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.1242i | − | 0.813595i | −0.913518 | − | 0.406797i | \(-0.866645\pi\) | ||
0.913518 | − | 0.406797i | \(-0.133355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.66310 | + | 4.66310i | −0.220557 | + | 0.220557i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1296i | 0.572431i | 0.958165 | + | 0.286215i | \(0.0923973\pi\) | ||||
−0.958165 | + | 0.286215i | \(0.907603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17135 | + | 3.17135i | 0.149333 | + | 0.149333i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.9089 | 1.45223 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.96532 | + | 3.96532i | −0.185490 | + | 0.185490i | −0.793743 | − | 0.608253i | \(-0.791871\pi\) |
0.608253 | + | 0.793743i | \(0.291871\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.2633 | − | 24.2633i | −1.13251 | − | 1.13251i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.6620 | + | 25.6620i | −1.19520 | + | 1.19520i | −0.219614 | + | 0.975587i | \(0.570480\pi\) |
−0.975587 | + | 0.219614i | \(0.929520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.98789 | + | 3.98789i | 0.185333 | + | 0.185333i | 0.793675 | − | 0.608342i | \(-0.208165\pi\) |
−0.608342 | + | 0.793675i | \(0.708165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.8576i | − | 0.502429i | −0.967931 | − | 0.251215i | \(-0.919170\pi\) | ||
0.967931 | − | 0.251215i | \(-0.0808300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.69253 | − | 6.69253i | 0.309032 | − | 0.309032i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.47009 | −0.436359 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.10878 | + | 7.10878i | 0.326862 | + | 0.326862i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.19819 | −0.192222 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.144583 | −0.00660618 | −0.00330309 | − | 0.999995i | \(-0.501051\pi\) | ||||
−0.00330309 | + | 0.999995i | \(0.501051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1551 | 0.463035 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.18999 | 0.281654 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9905 | + | 24.9905i | 1.13243 | + | 1.13243i | 0.989772 | + | 0.142655i | \(0.0455639\pi\) |
0.142655 | + | 0.989772i | \(0.454436\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.5857 | 1.29269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8603 | + | 16.8603i | −0.760893 | + | 0.760893i | −0.976484 | − | 0.215591i | \(-0.930832\pi\) |
0.215591 | + | 0.976484i | \(0.430832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 38.4707i | − | 1.73263i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.72168 | − | 6.72168i | −0.301509 | − | 0.301509i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2949 | − | 12.2949i | 0.550397 | − | 0.550397i | −0.376159 | − | 0.926555i | \(-0.622755\pi\) |
0.926555 | + | 0.376159i | \(0.122755\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.94182 | + | 8.94182i | 0.399491 | + | 0.399491i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.55961 | − | 2.55961i | 0.114128 | − | 0.114128i | −0.647737 | − | 0.761864i | \(-0.724284\pi\) |
0.761864 | + | 0.647737i | \(0.224284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.8356 | 1.81357 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.59987 | − | 6.59987i | −0.292534 | − | 0.292534i | 0.545547 | − | 0.838080i | \(-0.316322\pi\) |
−0.838080 | + | 0.545547i | \(0.816322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.3524i | − | 0.546440i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.45981 | − | 5.45981i | 0.241056 | − | 0.241056i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.17440i | 0.227570i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.4085i | 0.764147i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.9510i | − | 0.611204i | −0.952159 | − | 0.305602i | \(-0.901142\pi\) | ||
0.952159 | − | 0.305602i | \(-0.0988577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.6076i | 1.07601i | 0.842941 | + | 0.538007i | \(0.180822\pi\) | ||||
−0.842941 | + | 0.538007i | \(0.819178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −50.8237 | + | 50.8237i | −2.21391 | + | 2.21391i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4037i | 0.539291i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.55829 | − | 2.55829i | −0.111020 | − | 0.111020i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.2432 | −1.00678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.1847 | − | 29.1847i | 1.25941 | − | 1.25941i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.80430 | − | 4.80430i | −0.206936 | − | 0.206936i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4785 | + | 14.4785i | −0.622481 | + | 0.622481i | −0.946165 | − | 0.323684i | \(-0.895078\pi\) |
0.323684 | + | 0.946165i | \(0.395078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.7587 | − | 31.7587i | −1.36290 | − | 1.36290i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.5523i | − | 1.17805i | −0.808114 | − | 0.589026i | \(-0.799512\pi\) | ||
0.808114 | − | 0.589026i | \(-0.200488\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.776359 | − | 0.776359i | 0.0331342 | − | 0.0331342i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.65682 | 0.368793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.22565 | + | 1.22565i | 0.0521197 | + | 0.0521197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.5208 | −0.996608 | −0.498304 | − | 0.867002i | \(-0.666044\pi\) | ||||
−0.498304 | + | 0.867002i | \(0.666044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52.1011 | −2.20364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5619 | 0.657024 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3970 | 0.480327 | 0.240163 | − | 0.970732i | \(-0.422799\pi\) | ||||
0.240163 | + | 0.970732i | \(0.422799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.36212 | − | 7.36212i | −0.309180 | − | 0.309180i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2444 | 0.890613 | 0.445307 | − | 0.895378i | \(-0.353095\pi\) | ||||
0.445307 | + | 0.895378i | \(0.353095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.0980 | + | 23.0980i | −0.966622 | + | 0.966622i | −0.999461 | − | 0.0328390i | \(-0.989545\pi\) |
0.0328390 | + | 0.999461i | \(0.489545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.25601i | 0.303124i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.54721 | − | 8.54721i | −0.355825 | − | 0.355825i | 0.506446 | − | 0.862271i | \(-0.330959\pi\) |
−0.862271 | + | 0.506446i | \(0.830959\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.87817 | − | 6.87817i | 0.285847 | − | 0.285847i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0060 | − | 10.0060i | −0.415117 | − | 0.415117i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.93466 | + | 6.93466i | −0.287204 | + | 0.287204i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.9980 | −1.19687 | −0.598437 | − | 0.801170i | \(-0.704211\pi\) | ||||
−0.598437 | + | 0.801170i | \(0.704211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4365 | − | 11.4365i | −0.471234 | − | 0.471234i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.9523i | 0.944133i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.73827 | − | 1.73827i | 0.0713822 | − | 0.0713822i | −0.670514 | − | 0.741897i | \(-0.733927\pi\) |
0.741897 | + | 0.670514i | \(0.233927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 23.6334i | − | 0.967252i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.3429i | 0.953764i | 0.878967 | + | 0.476882i | \(0.158233\pi\) | ||||
−0.878967 | + | 0.476882i | \(0.841767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.2850i | − | 0.582697i | −0.956617 | − | 0.291348i | \(-0.905896\pi\) | ||
0.956617 | − | 0.291348i | \(-0.0941039\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.53367i | − | 0.184625i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.84325 | − | 4.84325i | 0.196581 | − | 0.196581i | −0.601951 | − | 0.798533i | \(-0.705610\pi\) |
0.798533 | + | 0.601951i | \(0.205610\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 10.0027i | − | 0.405328i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.9619 | − | 18.9619i | −0.767116 | − | 0.767116i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.37122 | −0.257331 | −0.128666 | − | 0.991688i | \(-0.541069\pi\) | ||||
−0.128666 | + | 0.991688i | \(0.541069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7251 | + | 13.7251i | −0.552553 | + | 0.552553i | −0.927177 | − | 0.374624i | \(-0.877772\pi\) |
0.374624 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.92352 | + | 6.92352i | 0.278280 | + | 0.278280i | 0.832422 | − | 0.554142i | \(-0.186954\pi\) |
−0.554142 | + | 0.832422i | \(0.686954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7994 | + | 10.7994i | −0.433365 | + | 0.433365i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.22944 | − | 3.22944i | −0.129385 | − | 0.129385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.50180i | 0.139848i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.89402 | + | 8.89402i | −0.354628 | + | 0.354628i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.299394 | −0.0119187 | −0.00595935 | − | 0.999982i | \(-0.501897\pi\) | ||||
−0.00595935 | + | 0.999982i | \(0.501897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.80606 | + | 4.80606i | 0.191024 | + | 0.191024i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.2113 | 1.39512 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.55342 | −0.180130 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.7708 | 1.80784 | 0.903920 | − | 0.427702i | \(-0.140677\pi\) | ||||
0.903920 | + | 0.427702i | \(0.140677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.26732 | −0.365467 | −0.182734 | − | 0.983162i | \(-0.558495\pi\) | ||||
−0.182734 | + | 0.983162i | \(0.558495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.284672 | − | 0.284672i | −0.0111916 | − | 0.0111916i | 0.701489 | − | 0.712680i | \(-0.252519\pi\) |
−0.712680 | + | 0.701489i | \(0.752519\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.45167 | −0.331757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2145 | + | 13.2145i | −0.517918 | + | 0.517918i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 11.1970i | − | 0.438173i | −0.975705 | − | 0.219087i | \(-0.929692\pi\) | ||
0.975705 | − | 0.219087i | \(-0.0703078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.18391 | − | 4.18391i | −0.163230 | − | 0.163230i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.66498 | − | 5.66498i | 0.220676 | − | 0.220676i | −0.588107 | − | 0.808783i | \(-0.700127\pi\) |
0.808783 | + | 0.588107i | \(0.200127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3785 | + | 23.3785i | 0.909320 | + | 0.909320i | 0.996217 | − | 0.0868975i | \(-0.0276953\pi\) |
−0.0868975 | + | 0.996217i | \(0.527695\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −57.0275 | + | 57.0275i | −2.21476 | + | 2.21476i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.1230 | −0.663006 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.8421 | − | 17.8421i | −0.689815 | − | 0.689815i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.56481i | − | 0.0990135i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.6324 | + | 26.6324i | −1.02660 | + | 1.02660i | −0.0269656 | + | 0.999636i | \(0.508584\pi\) |
−0.999636 | + | 0.0269656i | \(0.991416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5539i | 0.520918i | 0.965485 | + | 0.260459i | \(0.0838739\pi\) | ||||
−0.965485 | + | 0.260459i | \(0.916126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.42915i | − | 0.246728i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 23.9945i | − | 0.919470i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.3467i | 0.587225i | 0.955925 | + | 0.293613i | \(0.0948575\pi\) | ||||
−0.955925 | + | 0.293613i | \(0.905142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.66207 | + | 3.66207i | −0.139717 | + | 0.139717i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 50.8249i | − | 1.93627i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6170 | − | 10.6170i | −0.403891 | − | 0.403891i | 0.475710 | − | 0.879602i | \(-0.342191\pi\) |
−0.879602 | + | 0.475710i | \(0.842191\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.565835 | 0.0214943 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.3567 | − | 20.3567i | 0.771067 | − | 0.771067i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.8028 | + | 13.8028i | 0.522072 | + | 0.522072i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.96737 | + | 5.96737i | −0.225384 | + | 0.225384i | −0.810761 | − | 0.585377i | \(-0.800947\pi\) |
0.585377 | + | 0.810761i | \(0.300947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00137 | − | 2.00137i | −0.0754829 | − | 0.0754829i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 13.0213i | − | 0.489717i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3379 | − | 35.3379i | 1.32714 | − | 1.32714i | 0.419287 | − | 0.907854i | \(-0.362280\pi\) |
0.907854 | − | 0.419287i | \(-0.137720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.830280 | 0.0311379 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6212 | + | 22.6212i | 0.847172 | + | 0.847172i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.1256 | 0.751606 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.8418 | 1.41126 | 0.705631 | − | 0.708580i | \(-0.250664\pi\) | ||||
0.705631 | + | 0.708580i | \(0.250664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8066 | 0.476942 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.2046 | 1.01175 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3722 | − | 32.3722i | −1.20062 | − | 1.20062i | −0.973978 | − | 0.226641i | \(-0.927226\pi\) |
−0.226641 | − | 0.973978i | \(-0.572774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.2991 | 0.788855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.6309 | − | 45.6309i | 1.68772 | − | 1.68772i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.96701i | − | 0.0726532i | −0.999340 | − | 0.0363266i | \(-0.988434\pi\) | ||
0.999340 | − | 0.0363266i | \(-0.0115657\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.48881 | − | 7.48881i | −0.275854 | − | 0.275854i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3605 | − | 14.3605i | 0.528261 | − | 0.528261i | −0.391793 | − | 0.920054i | \(-0.628145\pi\) |
0.920054 | + | 0.391793i | \(0.128145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.8325 | − | 12.8325i | −0.471415 | − | 0.471415i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.28846 | + | 2.28846i | −0.0839556 | + | 0.0839556i | −0.747837 | − | 0.663882i | \(-0.768908\pi\) |
0.663882 | + | 0.747837i | \(0.268908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.77826 | −0.248004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.69253 | − | 6.69253i | −0.244540 | − | 0.244540i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7064i | 0.865058i | 0.901620 | + | 0.432529i | \(0.142379\pi\) | ||||
−0.901620 | + | 0.432529i | \(0.857621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.5975 | + | 22.5975i | −0.823497 | + | 0.823497i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.5469i | 1.11025i | 0.831768 | + | 0.555124i | \(0.187329\pi\) | ||||
−0.831768 | + | 0.555124i | \(0.812671\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6.92649i | − | 0.251416i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 23.6988i | − | 0.859080i | −0.903048 | − | 0.429540i | \(-0.858676\pi\) | ||
0.903048 | − | 0.429540i | \(-0.141324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.91306i | − | 0.214067i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.9716 | − | 30.9716i | 1.11832 | − | 1.11832i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.76629i | 0.0997548i | 0.998755 | + | 0.0498774i | \(0.0158831\pi\) | ||||
−0.998755 | + | 0.0498774i | \(0.984117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.8844 | − | 32.8844i | −1.18430 | − | 1.18430i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.0726 | −1.29744 | −0.648720 | − | 0.761027i | \(-0.724696\pi\) | ||||
−0.648720 | + | 0.761027i | \(0.724696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.31251 | + | 2.31251i | −0.0829608 | + | 0.0829608i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.58075 | + | 4.58075i | 0.164122 | + | 0.164122i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.52144 | + | 7.52144i | −0.269138 | + | 0.269138i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.4512 | + | 17.4512i | 0.623654 | + | 0.623654i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1024i | 0.431402i | 0.976459 | + | 0.215701i | \(0.0692037\pi\) | ||||
−0.976459 | + | 0.215701i | \(0.930796\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6129 | + | 22.6129i | −0.805039 | + | 0.805039i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.8163 | 0.384585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.39890 | + | 9.39890i | 0.333765 | + | 0.333765i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6614 | −0.838130 | −0.419065 | − | 0.907956i | \(-0.637642\pi\) | ||||
−0.419065 | + | 0.907956i | \(0.637642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2142 | 1.17503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.18770 | −0.0772984 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.8221 | −0.487773 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.5816 | − | 11.5816i | −0.407691 | − | 0.407691i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.5574 | −0.828235 | −0.414117 | − | 0.910223i | \(-0.635910\pi\) | ||||
−0.414117 | + | 0.910223i | \(0.635910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0698 | + | 14.0698i | −0.494056 | + | 0.494056i | −0.909581 | − | 0.415526i | \(-0.863598\pi\) |
0.415526 | + | 0.909581i | \(0.363598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.54627i | 0.334802i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2680 | + | 10.2680i | 0.359233 | + | 0.359233i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.07354 | + | 2.07354i | −0.0724552 | + | 0.0724552i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1332 | − | 28.1332i | −0.981855 | − | 0.981855i | 0.0179834 | − | 0.999838i | \(-0.494275\pi\) |
−0.999838 | + | 0.0179834i | \(0.994275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.6068 | + | 27.6068i | −0.962313 | + | 0.962313i | −0.999315 | − | 0.0370020i | \(-0.988219\pi\) |
0.0370020 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.79320 | 0.236223 | 0.118111 | − | 0.993000i | \(-0.462316\pi\) | ||||
0.118111 | + | 0.993000i | \(0.462316\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.7474 | − | 25.7474i | −0.894245 | − | 0.894245i | 0.100675 | − | 0.994919i | \(-0.467900\pi\) |
−0.994919 | + | 0.100675i | \(0.967900\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 8.69755i | − | 0.301715i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.8385 | + | 30.8385i | −1.06849 | + | 1.06849i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 46.1096i | − | 1.59378i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.4280i | 0.394538i | 0.980349 | + | 0.197269i | \(0.0632073\pi\) | ||||
−0.980349 | + | 0.197269i | \(0.936793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1.33022i | − | 0.0458696i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49.9387i | 1.71998i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.98522 | + | 6.98522i | −0.240015 | + | 0.240015i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.95983i | 0.135901i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.95866 | + | 3.95866i | 0.135701 | + | 0.135701i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.67475 | 0.331257 | 0.165629 | − | 0.986188i | \(-0.447035\pi\) | ||||
0.165629 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.5831 | + | 26.5831i | −0.908061 | + | 0.908061i | −0.996116 | − | 0.0880544i | \(-0.971935\pi\) |
0.0880544 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.58572 | + | 1.58572i | 0.0541040 | + | 0.0541040i | 0.733641 | − | 0.679537i | \(-0.237819\pi\) |
−0.679537 | + | 0.733641i | \(0.737819\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.29290 | − | 5.29290i | 0.180382 | − | 0.180382i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.59115 | − | 9.59115i | −0.326486 | − | 0.326486i | 0.524762 | − | 0.851249i | \(-0.324154\pi\) |
−0.851249 | + | 0.524762i | \(0.824154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 68.1426i | − | 2.31424i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.37147 | − | 1.37147i | 0.0465241 | − | 0.0465241i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.8864 | 1.85975 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.17763 | − | 2.17763i | −0.0737015 | − | 0.0737015i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.7116 | −1.10459 | −0.552295 | − | 0.833649i | \(-0.686248\pi\) | ||||
−0.552295 | + | 0.833649i | \(0.686248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.3661 | −0.990496 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.42337 | 0.317481 | 0.158741 | − | 0.987320i | \(-0.449257\pi\) | ||||
0.158741 | + | 0.987320i | \(0.449257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.1729 | −0.443304 | −0.221652 | − | 0.975126i | \(-0.571145\pi\) | ||||
−0.221652 | + | 0.975126i | \(0.571145\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.04550 | + | 7.04550i | 0.236565 | + | 0.236565i | 0.815426 | − | 0.578861i | \(-0.196503\pi\) |
−0.578861 | + | 0.815426i | \(0.696503\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.0394 | 0.370251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.23808 | + | 8.23808i | −0.275986 | + | 0.275986i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.47397i | 0.250107i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.3825 | + | 25.3825i | 0.847497 | + | 0.847497i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.5546 | − | 36.5546i | 1.21916 | − | 1.21916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.5131 | + | 44.5131i | 1.48295 | + | 1.48295i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.8644 | − | 11.8644i | 0.394821 | − | 0.394821i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.4995 | −1.51079 | −0.755394 | − | 0.655271i | \(-0.772554\pi\) | ||||
−0.755394 | + | 0.655271i | \(0.772554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.41047 | − | 4.41047i | −0.146286 | − | 0.146286i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.2904i | 1.36801i | 0.729477 | + | 0.684005i | \(0.239763\pi\) | ||||
−0.729477 | + | 0.684005i | \(0.760237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1965 | + | 11.1965i | −0.370549 | + | 0.370549i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.45674i | 0.0811288i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1715i | 0.665397i | 0.943033 | + | 0.332698i | \(0.107959\pi\) | ||||
−0.943033 | + | 0.332698i | \(0.892041\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 9.94759i | − | 0.327784i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 55.1255i | − | 1.81448i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.33774 | − | 4.33774i | 0.142470 | − | 0.142470i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.18969i | − | 0.268695i | −0.990934 | − | 0.134348i | \(-0.957106\pi\) | ||
0.990934 | − | 0.134348i | \(-0.0428939\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.93940 | − | 6.93940i | −0.227430 | − | 0.227430i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.5574 | −0.967667 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0511 | − | 33.0511i | 1.07973 | − | 1.07973i | 0.0831985 | − | 0.996533i | \(-0.473486\pi\) |
0.996533 | − | 0.0831985i | \(-0.0265136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.0117 | − | 27.0117i | −0.881495 | − | 0.881495i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6371 | − | 26.6371i | 0.868345 | − | 0.868345i | −0.123944 | − | 0.992289i | \(-0.539554\pi\) |
0.992289 | + | 0.123944i | \(0.0395544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.06063 | − | 9.06063i | −0.295055 | − | 0.295055i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.5777i | 1.22111i | 0.791973 | + | 0.610556i | \(0.209054\pi\) | ||||
−0.791973 | + | 0.610556i | \(0.790946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.6521 | − | 50.6521i | 1.64424 | − | 1.64424i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0546 | 0.326042 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.96284 | − | 7.96284i | −0.257942 | − | 0.257942i | 0.566275 | − | 0.824217i | \(-0.308384\pi\) |
−0.824217 | + | 0.566275i | \(0.808384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1928 | −0.361812 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.43952 | −0.0787763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.5846 | −2.11563 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.53367 | −0.146095 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6144 | + | 16.6144i | 0.534282 | + | 0.534282i | 0.921844 | − | 0.387562i | \(-0.126683\pi\) |
−0.387562 | + | 0.921844i | \(0.626683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.4778 | 0.722092 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.9269 | − | 17.9269i | 0.575301 | − | 0.575301i | −0.358304 | − | 0.933605i | \(-0.616645\pi\) |
0.933605 | + | 0.358304i | \(0.116645\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.43011i | 0.109964i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.0721 | + | 35.0721i | 1.12206 | + | 1.12206i | 0.991432 | + | 0.130625i | \(0.0416983\pi\) |
0.130625 | + | 0.991432i | \(0.458302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.61368 | + | 3.61368i | −0.115494 | + | 0.115494i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00282 | − | 2.00282i | −0.0639451 | − | 0.0639451i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.9265 | + | 24.9265i | −0.795033 | + | 0.795033i | −0.982308 | − | 0.187274i | \(-0.940035\pi\) |
0.187274 | + | 0.982308i | \(0.440035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.63592 | 0.274884 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.3100 | − | 20.3100i | −0.645819 | − | 0.645819i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.7686i | 0.342076i | 0.985264 | + | 0.171038i | \(0.0547121\pi\) | ||||
−0.985264 | + | 0.171038i | \(0.945288\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.42916 | + | 9.42916i | −0.299226 | + | 0.299226i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3858i | 0.328922i | 0.986384 | + | 0.164461i | \(0.0525885\pi\) | ||||
−0.986384 | + | 0.164461i | \(0.947412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.06906i | − | 0.255294i |
(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 | 1600.2.s.e.207.4 | 24 | ||
4.3 | odd | 2 | 400.2.s.e.107.11 | yes | 24 | ||
5.2 | odd | 4 | 1600.2.j.e.143.9 | 24 | |||
5.3 | odd | 4 | 1600.2.j.e.143.4 | 24 | |||
5.4 | even | 2 | inner | 1600.2.s.e.207.9 | 24 | ||
16.3 | odd | 4 | 1600.2.j.e.1007.9 | 24 | |||
16.13 | even | 4 | 400.2.j.e.307.5 | yes | 24 | ||
20.3 | even | 4 | 400.2.j.e.43.5 | ✓ | 24 | ||
20.7 | even | 4 | 400.2.j.e.43.8 | yes | 24 | ||
20.19 | odd | 2 | 400.2.s.e.107.2 | yes | 24 | ||
80.3 | even | 4 | inner | 1600.2.s.e.943.4 | 24 | ||
80.13 | odd | 4 | 400.2.s.e.243.11 | yes | 24 | ||
80.19 | odd | 4 | 1600.2.j.e.1007.4 | 24 | |||
80.29 | even | 4 | 400.2.j.e.307.8 | yes | 24 | ||
80.67 | even | 4 | inner | 1600.2.s.e.943.9 | 24 | ||
80.77 | odd | 4 | 400.2.s.e.243.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.e.43.5 | ✓ | 24 | 20.3 | even | 4 | ||
400.2.j.e.43.8 | yes | 24 | 20.7 | even | 4 | ||
400.2.j.e.307.5 | yes | 24 | 16.13 | even | 4 | ||
400.2.j.e.307.8 | yes | 24 | 80.29 | even | 4 | ||
400.2.s.e.107.2 | yes | 24 | 20.19 | odd | 2 | ||
400.2.s.e.107.11 | yes | 24 | 4.3 | odd | 2 | ||
400.2.s.e.243.2 | yes | 24 | 80.77 | odd | 4 | ||
400.2.s.e.243.11 | yes | 24 | 80.13 | odd | 4 | ||
1600.2.j.e.143.4 | 24 | 5.3 | odd | 4 | |||
1600.2.j.e.143.9 | 24 | 5.2 | odd | 4 | |||
1600.2.j.e.1007.4 | 24 | 80.19 | odd | 4 | |||
1600.2.j.e.1007.9 | 24 | 16.3 | odd | 4 | |||
1600.2.s.e.207.4 | 24 | 1.1 | even | 1 | trivial | ||
1600.2.s.e.207.9 | 24 | 5.4 | even | 2 | inner | ||
1600.2.s.e.943.4 | 24 | 80.3 | even | 4 | inner | ||
1600.2.s.e.943.9 | 24 | 80.67 | even | 4 | inner |