Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [780,2,Mod(73,780)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(780, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("780.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 780.r (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: | \(6.22833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.6 | ||
Character | \(\chi\) | \(=\) | 780.73 |
Dual form | 780.2.r.a.577.6 |
$q$-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 \(\left(\mathbb{Z}/780\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(301\) | \(391\) | \(521\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.62796 | + | 1.53289i | 0.728044 | + | 0.685531i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.13466i | − | 0.806826i | −0.915018 | − | 0.403413i | \(-0.867824\pi\) | ||
0.915018 | − | 0.403413i | \(-0.132176\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.89894 | − | 1.89894i | 0.572553 | − | 0.572553i | −0.360288 | − | 0.932841i | \(-0.617322\pi\) |
0.932841 | + | 0.360288i | \(0.117322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37361 | + | 3.33364i | 0.380972 | + | 0.924587i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0672190 | − | 2.23506i | −0.0173559 | − | 0.577089i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.22748 | − | 1.22748i | −0.297708 | − | 0.297708i | 0.542408 | − | 0.840115i | \(-0.317513\pi\) |
−0.840115 | + | 0.542408i | \(0.817513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.581270 | − | 0.581270i | 0.133352 | − | 0.133352i | −0.637280 | − | 0.770632i | \(-0.719941\pi\) |
0.770632 | + | 0.637280i | \(0.219941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50943 | + | 1.50943i | −0.329385 | + | 0.329385i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.10913 | − | 4.10913i | 0.856812 | − | 0.856812i | −0.134149 | − | 0.990961i | \(-0.542830\pi\) |
0.990961 | + | 0.134149i | \(0.0428300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.300476 | + | 4.99096i | 0.0600953 | + | 0.998193i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.81712i | − | 0.337431i | −0.985665 | − | 0.168715i | \(-0.946038\pi\) | ||
0.985665 | − | 0.168715i | \(-0.0539619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74497 | + | 4.74497i | 0.852223 | + | 0.852223i | 0.990407 | − | 0.138184i | \(-0.0441265\pi\) |
−0.138184 | + | 0.990407i | \(0.544127\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.68551 | −0.467487 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.27221 | − | 3.47513i | 0.553104 | − | 0.587405i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00961i | − | 0.987974i | −0.869469 | − | 0.493987i | \(-0.835539\pi\) | ||
0.869469 | − | 0.493987i | \(-0.164461\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.38595 | − | 3.32853i | 0.221930 | − | 0.532992i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85523 | + | 3.85523i | 0.602086 | + | 0.602086i | 0.940866 | − | 0.338780i | \(-0.110014\pi\) |
−0.338780 | + | 0.940866i | \(0.610014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.78653 | − | 3.78653i | 0.577440 | − | 0.577440i | −0.356757 | − | 0.934197i | \(-0.616118\pi\) |
0.934197 | + | 0.356757i | \(0.116118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.53289 | + | 1.62796i | −0.228510 | + | 0.242681i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.75112i | 0.401292i | 0.979664 | + | 0.200646i | \(0.0643041\pi\) | ||||
−0.979664 | + | 0.200646i | \(0.935696\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44322 | 0.349032 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.73592i | 0.243077i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79380 | − | 7.79380i | −1.07056 | − | 1.07056i | −0.997314 | − | 0.0732468i | \(-0.976664\pi\) |
−0.0732468 | − | 0.997314i | \(-0.523336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00227 | − | 0.180517i | 0.809346 | − | 0.0243409i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.822039 | −0.108882 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.434208 | + | 0.434208i | 0.0565290 | + | 0.0565290i | 0.734806 | − | 0.678277i | \(-0.237273\pi\) |
−0.678277 | + | 0.734806i | \(0.737273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1423 | 1.68270 | 0.841352 | − | 0.540488i | \(-0.181760\pi\) | ||||
0.841352 | + | 0.540488i | \(0.181760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.13466 | 0.268942 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.87394 | + | 7.53263i | −0.356469 | + | 0.934307i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27294 | 0.155515 | 0.0777573 | − | 0.996972i | \(-0.475224\pi\) | ||||
0.0777573 | + | 0.996972i | \(0.475224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.81118 | −0.699584 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.66190 | − | 1.66190i | −0.197231 | − | 0.197231i | 0.601581 | − | 0.798812i | \(-0.294538\pi\) |
−0.798812 | + | 0.601581i | \(0.794538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.637019 | −0.0745575 | −0.0372787 | − | 0.999305i | \(-0.511869\pi\) | ||||
−0.0372787 | + | 0.999305i | \(0.511869\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.31667 | − | 3.74161i | 0.382977 | − | 0.432044i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.05360 | − | 4.05360i | −0.461950 | − | 0.461950i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.837401i | − | 0.0942149i | −0.998890 | − | 0.0471075i | \(-0.985000\pi\) | ||
0.998890 | − | 0.0471075i | \(-0.0150003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.22354i | − | 0.573358i | −0.958027 | − | 0.286679i | \(-0.907449\pi\) | ||
0.958027 | − | 0.286679i | \(-0.0925513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.116687 | − | 3.87988i | −0.0126564 | − | 0.420832i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.28490 | + | 1.28490i | −0.137756 | + | 0.137756i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.92688 | − | 3.92688i | −0.416248 | − | 0.416248i | 0.467660 | − | 0.883908i | \(-0.345097\pi\) |
−0.883908 | + | 0.467660i | \(0.845097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.11620 | − | 2.93220i | 0.745981 | − | 0.307378i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 6.71041i | − | 0.695837i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.83731 | − | 0.0552566i | 0.188504 | − | 0.00566921i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15970 | 0.625422 | 0.312711 | − | 0.949848i | \(-0.398763\pi\) | ||||
0.312711 | + | 0.949848i | \(0.398763\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.89894 | + | 1.89894i | 0.190851 | + | 0.190851i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.93730i | 0.391776i | 0.980626 | + | 0.195888i | \(0.0627589\pi\) | ||||
−0.980626 | + | 0.195888i | \(0.937241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.97517 | − | 3.97517i | 0.391685 | − | 0.391685i | −0.483603 | − | 0.875288i | \(-0.660672\pi\) |
0.875288 | + | 0.483603i | \(0.160672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.77109 | + | 0.143490i | −0.465611 | + | 0.0140032i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.2103 | + | 11.2103i | −1.08375 | + | 1.08375i | −0.0875884 | + | 0.996157i | \(0.527916\pi\) |
−0.996157 | + | 0.0875884i | \(0.972084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.33542 | + | 8.33542i | −0.798388 | + | 0.798388i | −0.982841 | − | 0.184453i | \(-0.940949\pi\) |
0.184453 | + | 0.982841i | \(0.440949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.24944 | + | 4.24944i | −0.403339 | + | 0.403339i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.73416 | − | 4.73416i | −0.445353 | − | 0.445353i | 0.448453 | − | 0.893806i | \(-0.351975\pi\) |
−0.893806 | + | 0.448453i | \(0.851975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9883 | − | 0.390622i | 1.21117 | − | 0.0364257i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.33364 | + | 1.37361i | −0.308196 | + | 0.126991i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.62025 | + | 2.62025i | −0.240198 | + | 0.240198i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.78804i | 0.344367i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.45212i | − | 0.491601i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.16145 | + | 8.58566i | −0.640540 | + | 0.767925i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.26184 | − | 5.26184i | −0.466913 | − | 0.466913i | 0.434000 | − | 0.900913i | \(-0.357102\pi\) |
−0.900913 | + | 0.434000i | \(0.857102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.35496 | −0.471478 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.1234 | −1.84556 | −0.922779 | − | 0.385330i | \(-0.874088\pi\) | ||||
−0.922779 | + | 0.385330i | \(0.874088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.24081 | − | 1.24081i | −0.107592 | − | 0.107592i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23506 | − | 0.0672190i | 0.192363 | − | 0.00578529i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1203i | 1.12094i | 0.828175 | + | 0.560470i | \(0.189379\pi\) | ||||
−0.828175 | + | 0.560470i | \(0.810621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3191i | 1.63862i | 0.573349 | + | 0.819311i | \(0.305644\pi\) | ||||
−0.573349 | + | 0.819311i | \(0.694356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.94533 | − | 1.94533i | 0.163827 | − | 0.163827i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.93881 | + | 3.72199i | 0.747501 | + | 0.311248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.78545 | − | 2.95819i | 0.231319 | − | 0.245665i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.72762 | − | 1.72762i | −0.142492 | − | 0.142492i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.41550 | + | 3.41550i | −0.279808 | + | 0.279808i | −0.833032 | − | 0.553224i | \(-0.813397\pi\) |
0.553224 | + | 0.833032i | \(0.313397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.07740 | + | 9.07740i | −0.738709 | + | 0.738709i | −0.972328 | − | 0.233619i | \(-0.924943\pi\) |
0.233619 | + | 0.972328i | \(0.424943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.22748 | − | 1.22748i | 0.0992358 | − | 0.0992358i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.451067 | + | 14.9981i | 0.0362305 | + | 1.20468i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7071 | + | 16.7071i | −1.33337 | + | 1.33337i | −0.431035 | + | 0.902335i | \(0.641851\pi\) |
−0.902335 | + | 0.431035i | \(0.858149\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.0221i | 0.874109i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.77160 | − | 8.77160i | −0.691299 | − | 0.691299i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.73933 | −0.449539 | −0.224769 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224769 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.37189 | − | 4.11660i | −0.340351 | − | 0.320477i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.4964i | − | 0.967002i | −0.875344 | − | 0.483501i | \(-0.839365\pi\) | ||
0.875344 | − | 0.483501i | \(-0.160635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.22638 | + | 9.15827i | −0.709721 | + | 0.704483i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.581270 | + | 0.581270i | 0.0444508 | + | 0.0444508i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1397 | − | 12.1397i | 0.922966 | − | 0.922966i | −0.0742720 | − | 0.997238i | \(-0.523663\pi\) |
0.997238 | + | 0.0742720i | \(0.0236633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6540 | − | 0.641415i | 0.805368 | − | 0.0484865i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.614063i | − | 0.0461558i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.88220 | 0.290169 | 0.145085 | − | 0.989419i | \(-0.453655\pi\) | ||||
0.145085 | + | 0.989419i | \(0.453655\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9058i | 1.18227i | 0.806572 | + | 0.591136i | \(0.201320\pi\) | ||||
−0.806572 | + | 0.591136i | \(0.798680\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.29304 | − | 9.29304i | −0.686961 | − | 0.686961i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.21209 | − | 9.78338i | 0.677286 | − | 0.719288i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.66183 | −0.340906 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.50943 | − | 1.50943i | −0.109795 | − | 0.109795i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.96501 | −0.286898 | −0.143449 | − | 0.989658i | \(-0.545819\pi\) | ||||
−0.143449 | + | 0.989658i | \(0.545819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9136 | 1.21747 | 0.608734 | − | 0.793374i | \(-0.291678\pi\) | ||||
0.608734 | + | 0.793374i | \(0.291678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.35855 | − | 3.29419i | 0.526957 | − | 0.235902i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.1980 | −1.65279 | −0.826396 | − | 0.563089i | \(-0.809613\pi\) | ||||
−0.826396 | + | 0.563089i | \(0.809613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2812 | −1.72125 | −0.860625 | − | 0.509239i | \(-0.829927\pi\) | ||||
−0.860625 | + | 0.509239i | \(0.829927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.900106 | − | 0.900106i | −0.0634886 | − | 0.0634886i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.87894 | −0.272248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.366486 | + | 12.1858i | 0.0255965 | + | 0.851094i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.10913 | + | 4.10913i | 0.285604 | + | 0.285604i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.20760i | − | 0.152703i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.03724 | 0.622149 | 0.311075 | − | 0.950386i | \(-0.399311\pi\) | ||||
0.311075 | + | 0.950386i | \(0.399311\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.35028i | 0.161039i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.9686 | − | 0.359955i | 0.816255 | − | 0.0245487i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1289 | − | 10.1289i | 0.687595 | − | 0.687595i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.450441 | + | 0.450441i | 0.0304380 | + | 0.0304380i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.40590 | − | 5.77806i | 0.161838 | − | 0.388675i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.1082i | − | 1.68137i | −0.541527 | − | 0.840684i | \(-0.682153\pi\) | ||
0.541527 | − | 0.840684i | \(-0.317847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99096 | + | 0.300476i | −0.332731 | + | 0.0200318i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2921 | −0.683110 | −0.341555 | − | 0.939862i | \(-0.610954\pi\) | ||||
−0.341555 | + | 0.939862i | \(0.610954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.77751 | + | 1.77751i | 0.117461 | + | 0.117461i | 0.763394 | − | 0.645933i | \(-0.223532\pi\) |
−0.645933 | + | 0.763394i | \(0.723532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.73265i | 0.377181i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0627 | + | 14.0627i | −0.921280 | + | 0.921280i | −0.997120 | − | 0.0758398i | \(-0.975836\pi\) |
0.0758398 | + | 0.997120i | \(0.475836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.21717 | + | 4.47870i | −0.275098 | + | 0.292158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.592132 | + | 0.592132i | −0.0384631 | + | 0.0384631i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1880 | − | 21.1880i | 1.37054 | − | 1.37054i | 0.510901 | − | 0.859640i | \(-0.329312\pi\) |
0.859640 | − | 0.510901i | \(-0.170688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.79901 | − | 1.79901i | 0.115885 | − | 0.115885i | −0.646786 | − | 0.762671i | \(-0.723888\pi\) |
0.762671 | + | 0.646786i | \(0.223888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.97746 | + | 3.74520i | 0.254110 | + | 0.239272i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.73619 | + | 1.13931i | 0.174099 | + | 0.0724924i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.69360 | + | 3.69360i | −0.234072 | + | 0.234072i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.4291i | − | 1.22635i | −0.789946 | − | 0.613177i | \(-0.789891\pi\) | ||
0.789946 | − | 0.613177i | \(-0.210109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.6060i | − | 0.981140i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.66098 | + | 2.82600i | −0.166637 | + | 0.176971i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.19958 | − | 7.19958i | −0.449097 | − | 0.449097i | 0.445957 | − | 0.895054i | \(-0.352863\pi\) |
−0.895054 | + | 0.445957i | \(0.852863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8285 | −0.797123 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.81712 | 0.112477 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.21874 | + | 9.21874i | 0.568452 | + | 0.568452i | 0.931695 | − | 0.363243i | \(-0.118330\pi\) |
−0.363243 | + | 0.931695i | \(0.618330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.740894 | − | 24.6350i | −0.0455127 | − | 1.51332i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.55344i | 0.339865i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.62017i | 0.0987834i | 0.998779 | + | 0.0493917i | \(0.0157283\pi\) | ||||
−0.998779 | + | 0.0493917i | \(0.984272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.91766 | − | 6.91766i | 0.420218 | − | 0.420218i | −0.465061 | − | 0.885279i | \(-0.653968\pi\) |
0.885279 | + | 0.465061i | \(0.153968\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.10529 | − | 2.95854i | −0.430032 | − | 0.179059i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0481 | + | 8.90696i | 0.605926 | + | 0.537110i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.18506 | + | 7.18506i | 0.431709 | + | 0.431709i | 0.889209 | − | 0.457501i | \(-0.151255\pi\) |
−0.457501 | + | 0.889209i | \(0.651255\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.74497 | + | 4.74497i | −0.284074 | + | 0.284074i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6309 | − | 10.6309i | 0.634185 | − | 0.634185i | −0.314930 | − | 0.949115i | \(-0.601981\pi\) |
0.949115 | + | 0.314930i | \(0.101981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7919 | + | 12.7919i | −0.760399 | + | 0.760399i | −0.976394 | − | 0.215995i | \(-0.930700\pi\) |
0.215995 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.33824 | − | 1.26010i | −0.0792707 | − | 0.0746418i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.22962 | − | 8.22962i | 0.485779 | − | 0.485779i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.9866i | − | 0.822740i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.35556 | − | 4.35556i | −0.255328 | − | 0.255328i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.8122 | −0.982178 | −0.491089 | − | 0.871109i | \(-0.663401\pi\) | ||||
−0.491089 | + | 0.871109i | \(0.663401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0412767 | + | 1.37247i | 0.00240322 | + | 0.0799080i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.68551i | − | 0.155829i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3427 | + | 8.05402i | 1.11862 | + | 0.465776i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.08296 | − | 8.08296i | −0.465894 | − | 0.465894i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.78409 | − | 2.78409i | 0.159942 | − | 0.159942i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.3951 | + | 20.1458i | 1.22508 | + | 1.15355i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.6050i | − | 0.833551i | −0.909009 | − | 0.416775i | \(-0.863160\pi\) | ||
0.909009 | − | 0.416775i | \(-0.136840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.62174 | −0.319809 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4910i | 1.55887i | 0.626481 | + | 0.779436i | \(0.284494\pi\) | ||||
−0.626481 | + | 0.779436i | \(0.715506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.82784 | + | 4.82784i | 0.272886 | + | 0.272886i | 0.830261 | − | 0.557375i | \(-0.188191\pi\) |
−0.557375 | + | 0.830261i | \(0.688191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.47513 | + | 3.27221i | 0.195802 | + | 0.184368i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.3999 | −1.53893 | −0.769464 | − | 0.638690i | \(-0.779477\pi\) | ||||
−0.769464 | + | 0.638690i | \(0.779477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.45061 | − | 3.45061i | −0.193197 | − | 0.193197i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8538 | 0.884874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.42699 | −0.0794000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.2254 | + | 7.85733i | −0.900021 | + | 0.435846i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.7881 | 0.651881 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.87271 | 0.323773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.68185 | − | 5.68185i | −0.312303 | − | 0.312303i | 0.533498 | − | 0.845801i | \(-0.320877\pi\) |
−0.845801 | + | 0.533498i | \(0.820877\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00961 | 0.329325 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.07229 | + | 1.95128i | 0.113221 | + | 0.106610i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7975 | + | 15.7975i | 0.860544 | + | 0.860544i | 0.991401 | − | 0.130858i | \(-0.0417731\pi\) |
−0.130858 | + | 0.991401i | \(0.541773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.69512i | 0.363629i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0209 | 0.975885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1581i | − | 1.08843i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.46035 | − | 8.90793i | −0.509328 | − | 0.479587i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2806 | − | 17.2806i | 0.927670 | − | 0.927670i | −0.0698847 | − | 0.997555i | \(-0.522263\pi\) |
0.997555 | + | 0.0698847i | \(0.0222632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0865 | + | 19.0865i | 1.02168 | + | 1.02168i | 0.999760 | + | 0.0219165i | \(0.00697681\pi\) |
0.0219165 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.32853 | + | 1.38595i | 0.177664 | + | 0.0739766i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.0078i | 1.75683i | 0.477901 | + | 0.878414i | \(0.341398\pi\) | ||||
−0.477901 | + | 0.878414i | \(0.658602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.157983 | − | 5.25301i | −0.00838489 | − | 0.278801i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.70560 | 0.196121 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0109 | + | 15.0109i | 0.792247 | + | 0.792247i | 0.981859 | − | 0.189612i | \(-0.0607230\pi\) |
−0.189612 | + | 0.981859i | \(0.560723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3243i | 0.964434i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.67855 | − | 2.67855i | 0.140587 | − | 0.140587i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.03704 | − | 0.976483i | −0.0542811 | − | 0.0511114i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.95951 | + | 2.95951i | −0.154485 | + | 0.154485i | −0.780118 | − | 0.625633i | \(-0.784841\pi\) |
0.625633 | + | 0.780118i | \(0.284841\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.85523 | + | 3.85523i | −0.200695 | + | 0.200695i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.6371 | + | 16.6371i | −0.863756 | + | 0.863756i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.69960 | + | 3.69960i | 0.191558 | + | 0.191558i | 0.796369 | − | 0.604811i | \(-0.206751\pi\) |
−0.604811 | + | 0.796369i | \(0.706751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1349 | − | 1.00707i | 0.575003 | − | 0.0520048i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.05764 | − | 2.49602i | 0.311984 | − | 0.128552i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.73427 | − | 6.73427i | 0.345916 | − | 0.345916i | −0.512670 | − | 0.858586i | \(-0.671343\pi\) |
0.858586 | + | 0.512670i | \(0.171343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.44137i | 0.381233i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.7639i | − | 0.856597i | −0.903637 | − | 0.428299i | \(-0.859113\pi\) | ||
0.903637 | − | 0.428299i | \(-0.140887\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.385343 | − | 12.8128i | −0.0196389 | − | 0.653001i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.78653 | + | 3.78653i | 0.192480 | + | 0.192480i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.1793 | −1.02313 | −0.511566 | − | 0.859244i | \(-0.670934\pi\) | ||||
−0.511566 | + | 0.859244i | \(0.670934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0877 | −0.510159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.9365 | + | 14.9365i | 0.753446 | + | 0.753446i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.28365 | − | 1.36325i | 0.0645872 | − | 0.0685926i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.6617i | 1.33811i | 0.743213 | + | 0.669055i | \(0.233301\pi\) | ||||
−0.743213 | + | 0.669055i | \(0.766699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.75478i | 0.0878487i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.5935 | − | 21.5935i | 1.07833 | − | 1.07833i | 0.0816678 | − | 0.996660i | \(-0.473975\pi\) |
0.996660 | − | 0.0816678i | \(-0.0260246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.30030 | + | 22.3358i | −0.463281 | + | 1.11263i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.62796 | − | 1.53289i | −0.0808937 | − | 0.0761701i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4119 | − | 11.4119i | −0.565667 | − | 0.565667i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.53012 | − | 2.53012i | 0.125107 | − | 0.125107i | −0.641781 | − | 0.766888i | \(-0.721804\pi\) |
0.766888 | + | 0.641781i | \(0.221804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.27742 | − | 9.27742i | 0.457622 | − | 0.457622i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.926887 | − | 0.926887i | 0.0456091 | − | 0.0456091i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00713 | − | 8.50369i | 0.393054 | − | 0.417430i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6606 | − | 13.6606i | 0.668965 | − | 0.668965i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.4939i | − | 1.00119i | −0.865681 | − | 0.500596i | \(-0.833114\pi\) | ||
0.865681 | − | 0.500596i | \(-0.166886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7083 | − | 22.7083i | −1.10674 | − | 1.10674i | −0.993577 | − | 0.113160i | \(-0.963903\pi\) |
−0.113160 | − | 0.993577i | \(-0.536097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.75112 | −0.133764 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.75748 | − | 6.49513i | 0.279279 | − | 0.315060i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 28.0544i | − | 1.35765i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.68885 | − | 8.95254i | −0.178099 | − | 0.432233i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.07318 | − | 7.07318i | −0.340703 | − | 0.340703i | 0.515929 | − | 0.856632i | \(-0.327447\pi\) |
−0.856632 | + | 0.515929i | \(0.827447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.4138 | − | 27.4138i | 1.31742 | − | 1.31742i | 0.401614 | − | 0.915809i | \(-0.368449\pi\) |
0.915809 | − | 0.401614i | \(-0.131551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.06137 | + | 0.122145i | −0.194728 | + | 0.00585641i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.77702i | − | 0.228516i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.5366 | −1.79152 | −0.895762 | − | 0.444533i | \(-0.853370\pi\) | ||||
−0.895762 | + | 0.444533i | \(0.853370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.44322i | 0.116344i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.57913 | + | 6.57913i | 0.312584 | + | 0.312584i | 0.845910 | − | 0.533326i | \(-0.179058\pi\) |
−0.533326 | + | 0.845910i | \(0.679058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.373296 | − | 12.4123i | −0.0176959 | − | 0.588397i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.83024 | 0.228463 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5481 | − | 12.5481i | −0.592183 | − | 0.592183i | 0.346038 | − | 0.938221i | \(-0.387527\pi\) |
−0.938221 | + | 0.346038i | \(0.887527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6417 | 0.689452 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.8374 | 0.603153 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0796 | + | 6.13489i | 0.753824 | + | 0.287608i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.0694 | 0.985583 | 0.492791 | − | 0.870147i | \(-0.335977\pi\) | ||||
0.492791 | + | 0.870147i | \(0.335977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.73592 | −0.0810257 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1853 | − | 11.1853i | −0.520949 | − | 0.520949i | 0.396909 | − | 0.917858i | \(-0.370083\pi\) |
−0.917858 | + | 0.396909i | \(0.870083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6791 | −1.79757 | −0.898786 | − | 0.438389i | \(-0.855549\pi\) | ||||
−0.898786 | + | 0.438389i | \(0.855549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.2863 | − | 10.9242i | 0.477017 | − | 0.506600i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3530 | + | 13.3530i | 0.617904 | + | 0.617904i | 0.944993 | − | 0.327090i | \(-0.106068\pi\) |
−0.327090 | + | 0.944993i | \(0.606068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.71730i | − | 0.125473i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.6274 | 1.08869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 14.3808i | − | 0.661230i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.07575 | + | 2.72644i | 0.141125 | + | 0.125098i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.79380 | − | 7.79380i | 0.356854 | − | 0.356854i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.95863 | − | 1.95863i | −0.0894919 | − | 0.0894919i | 0.660944 | − | 0.750436i | \(-0.270156\pi\) |
−0.750436 | + | 0.660944i | \(0.770156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0339 | − | 8.25488i | 0.913467 | − | 0.376390i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.4049i | 0.564443i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0277 | + | 9.44216i | 0.455335 | + | 0.428746i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7479 | −0.804234 | −0.402117 | − | 0.915588i | \(-0.631725\pi\) | ||||
−0.402117 | + | 0.915588i | \(0.631725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.05832 | + | 4.05832i | 0.183524 | + | 0.183524i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6538i | 1.11261i | 0.830978 | + | 0.556306i | \(0.187782\pi\) | ||||
−0.830978 | + | 0.556306i | \(0.812218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23048 | + | 2.23048i | −0.100456 | + | 0.100456i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.180517 | + | 6.00227i | 0.00811364 | + | 0.269782i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.54759 | + | 3.54759i | −0.159131 | + | 0.159131i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.763548 | − | 0.763548i | 0.0341811 | − | 0.0341811i | −0.689810 | − | 0.723991i | \(-0.742306\pi\) |
0.723991 | + | 0.689810i | \(0.242306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.83631 | + | 8.83631i | −0.394777 | + | 0.394777i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.2923 | + | 17.2923i | 0.771026 | + | 0.771026i | 0.978286 | − | 0.207260i | \(-0.0664545\pi\) |
−0.207260 | + | 0.978286i | \(0.566454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.03546 | + | 6.40975i | −0.268574 | + | 0.285230i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9999 | + | 0.0481545i | 0.577346 | + | 0.00213862i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.2401 | − | 22.2401i | 0.985776 | − | 0.985776i | −0.0141241 | − | 0.999900i | \(-0.504496\pi\) |
0.999900 | + | 0.0141241i | \(0.00449598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35982i | 0.0601549i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.822039i | − | 0.0362939i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.5649 | − | 0.377887i | 0.553676 | − | 0.0166517i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.22421 | + | 5.22421i | 0.229761 | + | 0.229761i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.1682 | −0.753599 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.21481 | 0.140843 | 0.0704217 | − | 0.997517i | \(-0.477565\pi\) | ||||
0.0704217 | + | 0.997517i | \(0.477565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.33192 | + | 7.33192i | 0.320603 | + | 0.320603i | 0.848998 | − | 0.528396i | \(-0.177206\pi\) |
−0.528396 | + | 0.848998i | \(0.677206\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.98708 | − | 7.07998i | −0.348585 | − | 0.308996i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.6487i | − | 0.507426i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10.7699i | − | 0.468255i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.434208 | + | 0.434208i | −0.0188430 | + | 0.0188430i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.55638 | + | 18.1476i | −0.327303 | + | 0.786059i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.4342 | + | 1.06568i | −1.53195 | + | 0.0460733i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.74513 | − | 2.74513i | −0.118461 | − | 0.118461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.63954 | − | 4.63954i | 0.199839 | − | 0.199839i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.865604 | + | 0.865604i | −0.0372152 | + | 0.0372152i | −0.725470 | − | 0.688254i | \(-0.758377\pi\) |
0.688254 | + | 0.725470i | \(0.258377\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2471 | − | 11.2471i | 0.482661 | − | 0.482661i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.3470 | + | 0.792381i | −1.12858 | + | 0.0339419i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4611 | − | 14.4611i | 0.618311 | − | 0.618311i | −0.326787 | − | 0.945098i | \(-0.605966\pi\) |
0.945098 | + | 0.326787i | \(0.105966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1423i | 0.560901i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.05624 | − | 1.05624i | −0.0449972 | − | 0.0449972i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.78757 | −0.0760151 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.4318 | + | 0.403960i | −0.570149 | + | 0.0171471i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.5392i | 0.870272i | 0.900365 | + | 0.435136i | \(0.143300\pi\) | ||||
−0.900365 | + | 0.435136i | \(0.856700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.8242 | + | 7.42172i | 0.753882 | + | 0.313905i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.29641 | + | 3.29641i | 0.139174 | + | 0.139174i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.91042 | + | 3.91042i | −0.164804 | + | 0.164804i | −0.784691 | − | 0.619887i | \(-0.787179\pi\) |
0.619887 | + | 0.784691i | \(0.287179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.450039 | − | 14.9640i | −0.0189333 | − | 0.629539i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.13466i | 0.0896473i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.0908 | 1.21955 | 0.609775 | − | 0.792574i | \(-0.291260\pi\) | ||||
0.609775 | + | 0.792574i | \(0.291260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.8608i | 1.16594i | 0.812494 | + | 0.582969i | \(0.198109\pi\) | ||||
−0.812494 | + | 0.582969i | \(0.801891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.80368 | + | 2.80368i | 0.117126 | + | 0.117126i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.7432 | + | 19.2738i | 0.906754 | + | 0.803773i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1273 | 0.463235 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9597 | − | 11.9597i | −0.497029 | − | 0.497029i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.1505 | −0.462600 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.5999 | −1.22590 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.53263 | − | 2.87394i | −0.311436 | − | 0.118823i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0251 | −1.11545 | −0.557723 | − | 0.830027i | \(-0.688325\pi\) | ||||
−0.557723 | + | 0.830027i | \(0.688325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.51622 | 0.227292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.4035 | + | 16.4035i | 0.674750 | + | 0.674750i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2668 | 0.955454 | 0.477727 | − | 0.878508i | \(-0.341461\pi\) | ||||
0.477727 | + | 0.878508i | \(0.341461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.28222 | + | 0.249086i | −0.339538 | + | 0.0102115i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1694 | + | 17.1694i | 0.702698 | + | 0.702698i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.1115i | − | 1.43462i | −0.696756 | − | 0.717308i | \(-0.745374\pi\) | ||
0.696756 | − | 0.717308i | \(-0.254626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3510 | −0.463015 | −0.231508 | − | 0.972833i | \(-0.574366\pi\) | ||||
−0.231508 | + | 0.972833i | \(0.574366\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.27294i | 0.0518382i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.80666 | + | 6.16675i | −0.236074 | + | 0.250714i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.0768 | + | 25.0768i | −1.01784 | + | 1.01784i | −0.0179998 | + | 0.999838i | \(0.505730\pi\) |
−0.999838 | + | 0.0179998i | \(0.994270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.74282 | + | 2.74282i | 0.111145 | + | 0.111145i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.17125 | + | 3.77897i | −0.371029 | + | 0.152881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 32.7471i | − | 1.32264i | −0.750103 | − | 0.661322i | \(-0.769996\pi\) | ||
0.750103 | − | 0.661322i | \(-0.230004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.35752 | − | 8.87581i | 0.337008 | − | 0.357907i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.04921 | 0.122757 | 0.0613784 | − | 0.998115i | \(-0.480450\pi\) | ||||
0.0613784 | + | 0.998115i | \(0.480450\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.15135 | − | 2.15135i | −0.0864701 | − | 0.0864701i | 0.662549 | − | 0.749019i | \(-0.269475\pi\) |
−0.749019 | + | 0.662549i | \(0.769475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.81118i | − | 0.233195i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.38255 | + | 8.38255i | −0.335840 | + | 0.335840i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8194 | + | 2.99933i | −0.992777 | + | 0.119973i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.56101 | + | 1.56101i | −0.0623406 | + | 0.0623406i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.37667 | + | 7.37667i | −0.294127 | + | 0.294127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.1168 | + | 26.1168i | −1.03969 | + | 1.03969i | −0.0405145 | + | 0.999179i | \(0.512900\pi\) |
−0.999179 | + | 0.0405145i | \(0.987100\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.39029 | − | 6.39029i | −0.253991 | − | 0.253991i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.500201 | − | 16.6319i | −0.0198499 | − | 0.660016i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.35604 | + | 8.14483i | 0.132971 | + | 0.322710i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.66190 | − | 1.66190i | 0.0657437 | − | 0.0657437i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.0903i | − | 0.556534i | −0.960504 | − | 0.278267i | \(-0.910240\pi\) | ||
0.960504 | − | 0.278267i | \(-0.0897599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.89537i | − | 0.390235i | −0.980780 | − | 0.195118i | \(-0.937491\pi\) | ||
0.980780 | − | 0.195118i | \(-0.0625089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.71764 | − | 8.20858i | −0.343257 | − | 0.323213i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.48001 | − | 7.48001i | −0.294069 | − | 0.294069i | 0.544616 | − | 0.838685i | \(-0.316675\pi\) |
−0.838685 | + | 0.544616i | \(0.816675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.64907 | 0.0647317 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.3244 | −0.561419 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0579 | + | 10.0579i | 0.393595 | + | 0.393595i | 0.875967 | − | 0.482372i | \(-0.160225\pi\) |
−0.482372 | + | 0.875967i | \(0.660225\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.3879 | − | 32.3799i | −1.34365 | − | 1.26519i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.637019i | − | 0.0248525i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.4548i | 1.42008i | 0.704164 | + | 0.710038i | \(0.251322\pi\) | ||||
−0.704164 | + | 0.710038i | \(0.748678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.58265 | + | 6.58265i | −0.256035 | + | 0.256035i | −0.823439 | − | 0.567404i | \(-0.807948\pi\) |
0.567404 | + | 0.823439i | \(0.307948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.78693 | + | 2.38448i | −0.224746 | + | 0.0926055i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.117954 | − | 3.92202i | −0.00457407 | − | 0.152090i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.46678 | − | 7.46678i | −0.289115 | − | 0.289115i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7542 | + | 17.7542i | −0.686415 | + | 0.686415i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.9565 | − | 24.9565i | 0.963437 | − | 0.963437i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3834 | + | 10.3834i | −0.400252 | + | 0.400252i | −0.878322 | − | 0.478070i | \(-0.841337\pi\) |
0.478070 | + | 0.878322i | \(0.341337\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.74161 | + | 3.31667i | 0.144015 | + | 0.127659i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.0470 | + | 22.0470i | −0.847334 | + | 0.847334i | −0.989800 | − | 0.142466i | \(-0.954497\pi\) |
0.142466 | + | 0.989800i | \(0.454497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.1489i | − | 0.504607i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.27761 | + | 7.27761i | 0.278879 | + | 0.278879i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.6066 | −1.70682 | −0.853412 | − | 0.521237i | \(-0.825471\pi\) | ||||
−0.853412 | + | 0.521237i | \(0.825471\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.1120 | + | 21.3592i | −0.768438 | + | 0.816093i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.51377i | − | 0.0959064i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.2761 | − | 36.6874i | 0.581973 | − | 1.39768i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.1306 | − | 33.1306i | −1.26035 | − | 1.26035i | −0.950924 | − | 0.309424i | \(-0.899864\pi\) |
−0.309424 | − | 0.950924i | \(-0.600136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.05360 | − | 4.05360i | 0.153983 | − | 0.153983i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.6141 | + | 31.4506i | −1.12333 | + | 1.19299i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.46444i | − | 0.358491i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8877 | 0.752222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.40260i | 0.204053i | 0.994782 | + | 0.102027i | \(0.0325327\pi\) | ||||
−0.994782 | + | 0.102027i | \(0.967467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.49320 | − | 3.49320i | −0.131749 | − | 0.131749i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.14891 | − | 0.184927i | 0.231581 | − | 0.00696477i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.40480 | 0.316095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.9371 | + | 34.9371i | 1.31209 | + | 1.31209i | 0.919873 | + | 0.392216i | \(0.128292\pi\) |
0.392216 | + | 0.919873i | \(0.371708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.837401 | 0.0314050 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.9954 | 1.46039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.84657 | + | 19.7615i | 0.330843 | + | 0.739037i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.9644 | −1.11904 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4590 | 0.874872 | 0.437436 | − | 0.899249i | \(-0.355887\pi\) | ||||
0.437436 | + | 0.899249i | \(0.355887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.48564 | − | 8.48564i | −0.316022 | − | 0.316022i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.54419 | −0.0946194 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.06919 | − | 0.546002i | 0.336821 | − | 0.0202780i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.12835 | + | 8.12835i | 0.301464 | + | 0.301464i | 0.841586 | − | 0.540123i | \(-0.181622\pi\) |
−0.540123 | + | 0.841586i | \(0.681622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.29577 | −0.343817 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.4133i | − | 0.569303i | −0.958631 | − | 0.284652i | \(-0.908122\pi\) | ||
0.958631 | − | 0.284652i | \(-0.0918779\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.164231 | − | 5.46074i | −0.00605774 | − | 0.201422i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.41724 | − | 2.41724i | 0.0890403 | − | 0.0890403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.33555 | − | 6.33555i | −0.233057 | − | 0.233057i | 0.580910 | − | 0.813967i | \(-0.302697\pi\) |
−0.813967 | + | 0.580910i | \(0.802697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12916 | − | 2.74039i | −0.0414809 | − | 0.100671i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.7202i | 1.64063i | 0.571915 | + | 0.820313i | \(0.306201\pi\) | ||||
−0.571915 | + | 0.820313i | \(0.693799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7959 | + | 0.324684i | −0.395530 | + | 0.0118955i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.22354 | 0.191119 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.9303 | + | 23.9303i | 0.874394 | + | 0.874394i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.64023i | − | 0.169324i | −0.996410 | − | 0.0846621i | \(-0.973019\pi\) | ||
0.996410 | − | 0.0846621i | \(-0.0269811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7384 | + | 13.7384i | −0.500657 | + | 0.500657i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.6923 | + | 0.862916i | −1.04422 | + | 0.0314047i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4954 | + | 20.4954i | −0.744918 | + | 0.744918i | −0.973520 | − | 0.228602i | \(-0.926584\pi\) |
0.228602 | + | 0.973520i | \(0.426584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.0351 | + | 11.0351i | −0.400549 | + | 0.400549i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.6249 | − | 17.6249i | 0.638902 | − | 0.638902i | −0.311383 | − | 0.950285i | \(-0.600792\pi\) |
0.950285 | + | 0.311383i | \(0.100792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7933 | + | 17.7933i | 0.644160 | + | 0.644160i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.87988 | − | 0.116687i | 0.140277 | − | 0.00421881i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.851061 | + | 2.04393i | −0.0307300 | + | 0.0738020i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.6848 | − | 35.6848i | 1.28683 | − | 1.28683i | 0.350123 | − | 0.936704i | \(-0.386140\pi\) |
0.936704 | − | 0.350123i | \(-0.113860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1817i | 0.366687i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.4900i | 0.377301i | 0.982044 | + | 0.188650i | \(0.0604113\pi\) | ||||
−0.982044 | + | 0.188650i | \(0.939589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.2562 | + | 25.1077i | −0.799468 | + | 0.901897i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.07111 | + | 9.07111i | 0.325424 | + | 0.325424i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.48186 | 0.160579 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.31170 | −0.225850 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.28490 | − | 1.28490i | −0.0459185 | − | 0.0459185i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52.8085 | + | 1.58821i | −1.88482 | + | 0.0566856i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.0980i | − | 0.573832i | −0.957956 | − | 0.286916i | \(-0.907370\pi\) | ||
0.957956 | − | 0.286916i | \(-0.0926301\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 13.0373i | − | 0.464139i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.1058 | + | 10.1058i | −0.359322 | + | 0.359322i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0525 | + | 43.8119i | 0.641062 | + | 1.55581i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.8957 | + | 17.9435i | −0.599229 | + | 0.636390i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.8833 | + | 17.8833i | 0.633460 | + | 0.633460i | 0.948934 | − | 0.315474i | \(-0.102164\pi\) |
−0.315474 | + | 0.948934i | \(0.602164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.37694 | − | 3.37694i | 0.119468 | − | 0.119468i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.92688 | − | 3.92688i | 0.138749 | − | 0.138749i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.20966 | + | 1.20966i | −0.0426881 | + | 0.0426881i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.833845 | − | 27.7257i | −0.0293892 | − | 0.977202i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.14563 | − | 1.14563i | 0.0403282 | − | 0.0403282i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.4265i | − | 0.718157i | −0.933307 | − | 0.359079i | \(-0.883091\pi\) | ||
0.933307 | − | 0.359079i | \(-0.116909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.25247 | + | 4.25247i | 0.149325 | + | 0.149325i | 0.777816 | − | 0.628492i | \(-0.216327\pi\) |
−0.628492 | + | 0.777816i | \(0.716327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.78305 | −0.343106 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.34337 | − | 8.79778i | −0.327284 | − | 0.308173i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.40199i | − | 0.154006i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.93220 | + | 7.11620i | 0.102459 | + | 0.248660i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9521 | − | 26.9521i | −0.940636 | − | 0.940636i | 0.0576979 | − | 0.998334i | \(-0.481624\pi\) |
−0.998334 | + | 0.0576979i | \(0.981624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.9491 | + | 25.9491i | −0.904528 | + | 0.904528i | −0.995824 | − | 0.0912955i | \(-0.970899\pi\) |
0.0912955 | + | 0.995824i | \(0.470899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.806933 | − | 13.4033i | −0.0280938 | − | 0.466642i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.6260i | − | 1.58657i | −0.608848 | − | 0.793287i | \(-0.708368\pi\) | ||
0.608848 | − | 0.793287i | \(-0.291632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.7307 | −1.48410 | −0.742049 | − | 0.670346i | \(-0.766146\pi\) | ||||
−0.742049 | + | 0.670346i | \(0.766146\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 10.1612i | − | 0.352489i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.99900 | − | 2.99900i | −0.103909 | − | 0.103909i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1557 | − | 20.3436i | 0.662910 | − | 0.704020i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.71041 | 0.231946 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.57427 | + | 3.57427i | 0.123398 | + | 0.123398i | 0.766109 | − | 0.642711i | \(-0.222190\pi\) |
−0.642711 | + | 0.766109i | \(0.722190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6981 | 0.886140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.0343 | −0.517810 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.0588 | + | 0.766212i | −0.999653 | + | 0.0263585i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.08617 | 0.277844 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.0905 | 0.620863 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.6943 | − | 24.6943i | −0.846508 | − | 0.846508i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6644 | −0.365141 | −0.182571 | − | 0.983193i | \(-0.558442\pi\) | ||||
−0.182571 | + | 0.983193i | \(0.558442\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0552566 | + | 1.83731i | 0.00188974 | + | 0.0628345i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.7615 | + | 17.7615i | 0.606720 | + | 0.606720i | 0.942087 | − | 0.335367i | \(-0.108860\pi\) |
−0.335367 | + | 0.942087i | \(0.608860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.529028i | − | 0.0180502i | −0.999959 | − | 0.00902510i | \(-0.997127\pi\) | ||
0.999959 | − | 0.00902510i | \(-0.00287282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6384 | −0.396637 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5919i | 0.564795i | 0.959298 | + | 0.282397i | \(0.0911296\pi\) | ||||
−0.959298 | + | 0.282397i | \(0.908870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.3718 | − | 1.15403i | 1.30468 | − | 0.0392381i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.89001 | + | 9.89001i | −0.335882 | + | 0.335882i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.59018 | − | 1.59018i | −0.0539430 | − | 0.0539430i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.74853 | + | 4.24353i | 0.0592466 | + | 0.143787i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.15970i | 0.208474i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.3275 | + | 15.2873i | 0.619582 | + | 0.516804i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.7095 | −1.07075 | −0.535377 | − | 0.844613i | \(-0.679830\pi\) | ||||
−0.535377 | + | 0.844613i | \(0.679830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.8880 | + | 11.8880i | 0.400973 | + | 0.400973i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 45.8764i | − | 1.54561i | −0.634641 | − | 0.772807i | \(-0.718852\pi\) | ||
0.634641 | − | 0.772807i | \(-0.281148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.59797 | + | 7.59797i | −0.255692 | + | 0.255692i | −0.823299 | − | 0.567607i | \(-0.807869\pi\) |
0.567607 | + | 0.823299i | \(0.307869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.941292 | − | 0.999666i | 0.0316412 | − | 0.0336034i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.01004 | + | 2.01004i | −0.0674905 | + | 0.0674905i | −0.740046 | − | 0.672556i | \(-0.765196\pi\) |
0.672556 | + | 0.740046i | \(0.265196\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.2323 | + | 11.2323i | −0.376718 | + | 0.376718i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.89894 | + | 1.89894i | −0.0636170 | + | 0.0636170i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.59914 | + | 1.59914i | 0.0535132 | + | 0.0535132i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.32004 | + | 5.95099i | 0.211256 | + | 0.198920i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.98232 | − | 19.3724i | −0.266522 | − | 0.646826i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.62219 | − | 8.62219i | 0.287566 | − | 0.287566i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.1335i | 0.637428i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.4310i | 0.380401i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.3820 | + | 25.8940i | −0.810484 | + | 0.860746i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.3483 | + | 24.3483i | 0.808472 | + | 0.808472i | 0.984403 | − | 0.175931i | \(-0.0562934\pi\) |
−0.175931 | + | 0.984403i | \(0.556293\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.93730 | −0.130592 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.9116 | −1.38859 | −0.694297 | − | 0.719689i | \(-0.744284\pi\) | ||||
−0.694297 | + | 0.719689i | \(0.744284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.91920 | − | 9.91920i | −0.328278 | − | 0.328278i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.883414 | − | 29.3739i | −0.0292048 | − | 0.971070i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.0912i | 1.48904i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6303i | 1.04339i | 0.853133 | + | 0.521693i | \(0.174699\pi\) | ||||
−0.853133 | + | 0.521693i | \(0.825301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3273 | + | 10.3273i | −0.340296 | + | 0.340296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.25737 | − | 7.82299i | 0.107218 | − | 0.257497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.9937 | − | 1.80575i | 0.986188 | − | 0.0593726i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.97517 | + | 3.97517i | 0.130562 | + | 0.130562i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6715 | − | 19.6715i | 0.645400 | − | 0.645400i | −0.306477 | − | 0.951878i | \(-0.599150\pi\) |
0.951878 | + | 0.306477i | \(0.0991504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.42017 | − | 1.42017i | 0.0465442 | − | 0.0465442i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.4391 | − | 19.4391i | 0.636407 | − | 0.636407i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.58924 | − | 7.14608i | −0.248195 | − | 0.233702i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.54342 | − | 9.54342i | 0.311770 | − | 0.311770i | −0.533825 | − | 0.845595i | \(-0.679246\pi\) |
0.845595 | + | 0.533825i | \(0.179246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 6.82759i | − | 0.222810i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4194 | + | 10.4194i | 0.339662 | + | 0.339662i | 0.856240 | − | 0.516578i | \(-0.172794\pi\) |
−0.516578 | + | 0.856240i | \(0.672794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.6833 | 1.03175 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.143490 | − | 4.77109i | −0.00466772 | − | 0.155204i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.83373i | 0.124580i | 0.998058 | + | 0.0622898i | \(0.0198403\pi\) | ||||
−0.998058 | + | 0.0622898i | \(0.980160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.875018 | − | 2.12360i | −0.0284043 | − | 0.0689349i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.3746 | + | 19.3746i | 0.628265 | + | 0.628265i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.0921 | + | 27.0921i | −0.877598 | + | 0.877598i | −0.993286 | − | 0.115687i | \(-0.963093\pi\) |
0.115687 | + | 0.993286i | \(0.463093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.45486 | − | 6.07794i | −0.208874 | − | 0.196677i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.87990i | 0.157745i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.0073 | 0.904403 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0296i | 0.452566i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.2103 | − | 11.2103i | −0.361248 | − | 0.361248i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.5346 | + | 25.9268i | 0.886370 | + | 0.834612i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.6472 | 1.95028 | 0.975141 | − | 0.221586i | \(-0.0711234\pi\) | ||||
0.975141 | + | 0.221586i | \(0.0711234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.00904 | + | 1.00904i | 0.0324149 | + | 0.0324149i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1997 | −0.680331 | −0.340165 | − | 0.940366i | \(-0.610483\pi\) | ||||
−0.340165 | + | 0.940366i | \(0.610483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.2397 | 1.32208 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.0290 | + | 5.91709i | 0.545366 | + | 0.189499i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6849 | 0.789739 | 0.394869 | − | 0.918737i | \(-0.370790\pi\) | ||||
0.394869 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.9138 | −0.476648 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.33542 | − | 8.33542i | −0.266129 | − | 0.266129i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.5810 | −1.13486 | −0.567428 | − | 0.823423i | \(-0.692062\pi\) | ||||
−0.567428 | + | 0.823423i | \(0.692062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.7654 | − | 35.5601i | −1.20330 | − | 1.13304i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.15263 | − | 4.15263i | −0.132180 | − | 0.132180i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 31.1187i | − | 0.989516i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.07037 | −0.161065 | −0.0805327 | − | 0.996752i | \(-0.525662\pi\) | ||||
−0.0805327 | + | 0.996752i | \(0.525662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.03535i | 0.254994i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.5287 | − | 37.2205i | −1.25315 | − | 1.17997i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.7495 | − | 21.7495i | 0.688814 | − | 0.688814i | −0.273156 | − | 0.961970i | \(-0.588067\pi\) |
0.961970 | + | 0.273156i | \(0.0880674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.24944 | − | 4.24944i | −0.134446 | − | 0.134446i |
(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 | 780.2.r.a.73.6 | ✓ | 28 | |
3.2 | odd | 2 | 2340.2.u.i.73.5 | 28 | |||
5.2 | odd | 4 | 780.2.bm.a.697.6 | yes | 28 | ||
5.3 | odd | 4 | 3900.2.bm.b.2257.12 | 28 | |||
5.4 | even | 2 | 3900.2.r.b.3193.12 | 28 | |||
13.5 | odd | 4 | 780.2.bm.a.733.6 | yes | 28 | ||
15.2 | even | 4 | 2340.2.bp.i.1477.3 | 28 | |||
39.5 | even | 4 | 2340.2.bp.i.1513.3 | 28 | |||
65.18 | even | 4 | 3900.2.r.b.1357.12 | 28 | |||
65.44 | odd | 4 | 3900.2.bm.b.2293.12 | 28 | |||
65.57 | even | 4 | inner | 780.2.r.a.577.6 | yes | 28 | |
195.122 | odd | 4 | 2340.2.u.i.577.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
780.2.r.a.73.6 | ✓ | 28 | 1.1 | even | 1 | trivial | |
780.2.r.a.577.6 | yes | 28 | 65.57 | even | 4 | inner | |
780.2.bm.a.697.6 | yes | 28 | 5.2 | odd | 4 | ||
780.2.bm.a.733.6 | yes | 28 | 13.5 | odd | 4 | ||
2340.2.u.i.73.5 | 28 | 3.2 | odd | 2 | |||
2340.2.u.i.577.5 | 28 | 195.122 | odd | 4 | |||
2340.2.bp.i.1477.3 | 28 | 15.2 | even | 4 | |||
2340.2.bp.i.1513.3 | 28 | 39.5 | even | 4 | |||
3900.2.r.b.1357.12 | 28 | 65.18 | even | 4 | |||
3900.2.r.b.3193.12 | 28 | 5.4 | even | 2 | |||
3900.2.bm.b.2257.12 | 28 | 5.3 | odd | 4 | |||
3900.2.bm.b.2293.12 | 28 | 65.44 | odd | 4 |