Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,2,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("354.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.82670423155\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.41542366334681088.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.5 | ||
Root | \(-0.0738304 - 1.73048i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.2.c.a.353.6 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.0738304 | − | 1.73048i | 0.0426260 | − | 0.999091i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 2.30520i | − | 1.03092i | −0.856914 | − | 0.515459i | \(-0.827621\pi\) | ||
0.856914 | − | 0.515459i | \(-0.172379\pi\) | |||||||
\(6\) | −0.0738304 | + | 1.73048i | −0.0301411 | + | 0.706464i | ||||
\(7\) | 3.25240 | 1.22929 | 0.614647 | − | 0.788803i | \(-0.289299\pi\) | ||||
0.614647 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.98910 | − | 0.255524i | −0.996366 | − | 0.0851745i | ||||
\(10\) | 2.30520i | 0.728969i | ||||||||
\(11\) | 4.56636 | 1.37681 | 0.688405 | − | 0.725327i | \(-0.258311\pi\) | ||||
0.688405 | + | 0.725327i | \(0.258311\pi\) | |||||||
\(12\) | 0.0738304 | − | 1.73048i | 0.0213130 | − | 0.499546i | ||||
\(13\) | − | 2.44397i | − | 0.677834i | −0.940816 | − | 0.338917i | \(-0.889939\pi\) | ||
0.940816 | − | 0.338917i | \(-0.110061\pi\) | |||||||
\(14\) | −3.25240 | −0.869242 | ||||||||
\(15\) | −3.98910 | − | 0.170194i | −1.02998 | − | 0.0439439i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.52929i | 0.613444i | 0.951799 | + | 0.306722i | \(0.0992322\pi\) | ||||
−0.951799 | + | 0.306722i | \(0.900768\pi\) | |||||||
\(18\) | 2.98910 | + | 0.255524i | 0.704537 | + | 0.0602275i | ||||
\(19\) | −1.31396 | −0.301442 | −0.150721 | − | 0.988576i | \(-0.548160\pi\) | ||||
−0.150721 | + | 0.988576i | \(0.548160\pi\) | |||||||
\(20\) | − | 2.30520i | − | 0.515459i | ||||||
\(21\) | 0.240126 | − | 5.62821i | 0.0523998 | − | 1.22818i | ||||
\(22\) | −4.56636 | −0.973551 | ||||||||
\(23\) | −8.45845 | −1.76371 | −0.881854 | − | 0.471522i | \(-0.843705\pi\) | ||||
−0.881854 | + | 0.471522i | \(0.843705\pi\) | |||||||
\(24\) | −0.0738304 | + | 1.73048i | −0.0150706 | + | 0.353232i | ||||
\(25\) | −0.313957 | −0.0627913 | ||||||||
\(26\) | 2.44397i | 0.479301i | ||||||||
\(27\) | −0.662864 | + | 5.15370i | −0.127568 | + | 0.991830i | ||||
\(28\) | 3.25240 | 0.614647 | ||||||||
\(29\) | − | 7.58278i | − | 1.40809i | −0.710157 | − | 0.704043i | \(-0.751376\pi\) | ||
0.710157 | − | 0.704043i | \(-0.248624\pi\) | |||||||
\(30\) | 3.98910 | + | 0.170194i | 0.728306 | + | 0.0310730i | ||||
\(31\) | 1.81032i | 0.325144i | 0.986697 | + | 0.162572i | \(0.0519789\pi\) | ||||
−0.986697 | + | 0.162572i | \(0.948021\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.337136 | − | 7.90198i | 0.0586879 | − | 1.37556i | ||||
\(34\) | − | 2.52929i | − | 0.433770i | ||||||
\(35\) | − | 7.49745i | − | 1.26730i | ||||||
\(36\) | −2.98910 | − | 0.255524i | −0.498183 | − | 0.0425873i | ||||
\(37\) | 2.83361i | 0.465843i | 0.972496 | + | 0.232921i | \(0.0748285\pi\) | ||||
−0.972496 | + | 0.232921i | \(0.925172\pi\) | |||||||
\(38\) | 1.31396 | 0.213152 | ||||||||
\(39\) | −4.22922 | − | 0.180439i | −0.677218 | − | 0.0288934i | ||||
\(40\) | 2.30520i | 0.364484i | ||||||||
\(41\) | 5.77722i | 0.902250i | 0.892461 | + | 0.451125i | \(0.148977\pi\) | ||||
−0.892461 | + | 0.451125i | \(0.851023\pi\) | |||||||
\(42\) | −0.240126 | + | 5.62821i | −0.0370523 | + | 0.868451i | ||||
\(43\) | − | 11.5497i | − | 1.76131i | −0.473760 | − | 0.880654i | \(-0.657103\pi\) | ||
0.473760 | − | 0.880654i | \(-0.342897\pi\) | |||||||
\(44\) | 4.56636 | 0.688405 | ||||||||
\(45\) | −0.589033 | + | 6.89048i | −0.0878079 | + | 1.02717i | ||||
\(46\) | 8.45845 | 1.24713 | ||||||||
\(47\) | 0.674272 | 0.0983527 | 0.0491764 | − | 0.998790i | \(-0.484340\pi\) | ||||
0.0491764 | + | 0.998790i | \(0.484340\pi\) | |||||||
\(48\) | 0.0738304 | − | 1.73048i | 0.0106565 | − | 0.249773i | ||||
\(49\) | 3.57813 | 0.511162 | ||||||||
\(50\) | 0.313957 | 0.0444002 | ||||||||
\(51\) | 4.37689 | + | 0.186739i | 0.612887 | + | 0.0261487i | ||||
\(52\) | − | 2.44397i | − | 0.338917i | ||||||
\(53\) | 8.22118i | 1.12927i | 0.825342 | + | 0.564633i | \(0.190982\pi\) | ||||
−0.825342 | + | 0.564633i | \(0.809018\pi\) | |||||||
\(54\) | 0.662864 | − | 5.15370i | 0.0902043 | − | 0.701330i | ||||
\(55\) | − | 10.5264i | − | 1.41938i | ||||||
\(56\) | −3.25240 | −0.434621 | ||||||||
\(57\) | −0.0970099 | + | 2.27377i | −0.0128493 | + | 0.301168i | ||||
\(58\) | 7.58278i | 0.995668i | ||||||||
\(59\) | 7.51658 | + | 1.58147i | 0.978575 | + | 0.205890i | ||||
\(60\) | −3.98910 | − | 0.170194i | −0.514990 | − | 0.0219719i | ||||
\(61\) | 0.133657i | 0.0171130i | 0.999963 | + | 0.00855650i | \(0.00272365\pi\) | ||||
−0.999963 | + | 0.00855650i | \(0.997276\pi\) | |||||||
\(62\) | − | 1.81032i | − | 0.229911i | ||||||
\(63\) | −9.72175 | − | 0.831066i | −1.22483 | − | 0.104704i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.63383 | −0.698791 | ||||||||
\(66\) | −0.337136 | + | 7.90198i | −0.0414986 | + | 0.972666i | ||||
\(67\) | − | 3.33360i | − | 0.407264i | −0.979048 | − | 0.203632i | \(-0.934725\pi\) | ||
0.979048 | − | 0.203632i | \(-0.0652745\pi\) | |||||||
\(68\) | 2.52929i | 0.306722i | ||||||||
\(69\) | −0.624491 | + | 14.6371i | −0.0751798 | + | 1.76211i | ||||
\(70\) | 7.49745i | 0.896116i | ||||||||
\(71\) | 6.35743i | 0.754488i | 0.926114 | + | 0.377244i | \(0.123128\pi\) | ||||
−0.926114 | + | 0.377244i | \(0.876872\pi\) | |||||||
\(72\) | 2.98910 | + | 0.255524i | 0.352269 | + | 0.0301137i | ||||
\(73\) | 13.4703i | 1.57658i | 0.615302 | + | 0.788292i | \(0.289034\pi\) | ||||
−0.615302 | + | 0.788292i | \(0.710966\pi\) | |||||||
\(74\) | − | 2.83361i | − | 0.329401i | ||||||
\(75\) | −0.0231795 | + | 0.543295i | −0.00267654 | + | 0.0627343i | ||||
\(76\) | −1.31396 | −0.150721 | ||||||||
\(77\) | 14.8516 | 1.69250 | ||||||||
\(78\) | 4.22922 | + | 0.180439i | 0.478865 | + | 0.0204307i | ||||
\(79\) | 11.0366 | 1.24171 | 0.620856 | − | 0.783925i | \(-0.286785\pi\) | ||||
0.620856 | + | 0.783925i | \(0.286785\pi\) | |||||||
\(80\) | − | 2.30520i | − | 0.257729i | ||||||
\(81\) | 8.86942 | + | 1.52757i | 0.985491 | + | 0.169730i | ||||
\(82\) | − | 5.77722i | − | 0.637987i | ||||||
\(83\) | −9.52592 | −1.04561 | −0.522803 | − | 0.852454i | \(-0.675114\pi\) | ||||
−0.522803 | + | 0.852454i | \(0.675114\pi\) | |||||||
\(84\) | 0.240126 | − | 5.62821i | 0.0261999 | − | 0.614088i | ||||
\(85\) | 5.83054 | 0.632410 | ||||||||
\(86\) | 11.5497i | 1.24543i | ||||||||
\(87\) | −13.1218 | − | 0.559839i | −1.40681 | − | 0.0600211i | ||||
\(88\) | −4.56636 | −0.486776 | ||||||||
\(89\) | 4.28529 | 0.454240 | 0.227120 | − | 0.973867i | \(-0.427069\pi\) | ||||
0.227120 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(90\) | 0.589033 | − | 6.89048i | 0.0620896 | − | 0.726320i | ||||
\(91\) | − | 7.94876i | − | 0.833257i | ||||||
\(92\) | −8.45845 | −0.881854 | ||||||||
\(93\) | 3.13272 | + | 0.133657i | 0.324848 | + | 0.0138596i | ||||
\(94\) | −0.674272 | −0.0695459 | ||||||||
\(95\) | 3.02894i | 0.310762i | ||||||||
\(96\) | −0.0738304 | + | 1.73048i | −0.00753528 | + | 0.176616i | ||||
\(97\) | 8.58240i | 0.871411i | 0.900089 | + | 0.435706i | \(0.143501\pi\) | ||||
−0.900089 | + | 0.435706i | \(0.856499\pi\) | |||||||
\(98\) | −3.57813 | −0.361446 | ||||||||
\(99\) | −13.6493 | − | 1.16681i | −1.37181 | − | 0.117269i | ||||
\(100\) | −0.313957 | −0.0313957 | ||||||||
\(101\) | 8.85165 | 0.880772 | 0.440386 | − | 0.897809i | \(-0.354842\pi\) | ||||
0.440386 | + | 0.897809i | \(0.354842\pi\) | |||||||
\(102\) | −4.37689 | − | 0.186739i | −0.433376 | − | 0.0184899i | ||||
\(103\) | − | 13.6040i | − | 1.34044i | −0.742162 | − | 0.670221i | \(-0.766200\pi\) | ||
0.742162 | − | 0.670221i | \(-0.233800\pi\) | |||||||
\(104\) | 2.44397i | 0.239651i | ||||||||
\(105\) | −12.9742 | − | 0.553540i | −1.26615 | − | 0.0540199i | ||||
\(106\) | − | 8.22118i | − | 0.798512i | ||||||
\(107\) | 11.2988i | 1.09230i | 0.837689 | + | 0.546148i | \(0.183906\pi\) | ||||
−0.837689 | + | 0.546148i | \(0.816094\pi\) | |||||||
\(108\) | −0.662864 | + | 5.15370i | −0.0637841 | + | 0.495915i | ||||
\(109\) | 19.2424i | 1.84309i | 0.388269 | + | 0.921546i | \(0.373073\pi\) | ||||
−0.388269 | + | 0.921546i | \(0.626927\pi\) | |||||||
\(110\) | 10.5264i | 1.00365i | ||||||||
\(111\) | 4.90350 | + | 0.209207i | 0.465419 | + | 0.0198570i | ||||
\(112\) | 3.25240 | 0.307323 | ||||||||
\(113\) | 9.70743 | 0.913198 | 0.456599 | − | 0.889673i | \(-0.349067\pi\) | ||||
0.456599 | + | 0.889673i | \(0.349067\pi\) | |||||||
\(114\) | 0.0970099 | − | 2.27377i | 0.00908581 | − | 0.212958i | ||||
\(115\) | 19.4984i | 1.81824i | ||||||||
\(116\) | − | 7.58278i | − | 0.704043i | ||||||
\(117\) | −0.624491 | + | 7.30525i | −0.0577342 | + | 0.675371i | ||||
\(118\) | −7.51658 | − | 1.58147i | −0.691957 | − | 0.145586i | ||||
\(119\) | 8.22629i | 0.754103i | ||||||||
\(120\) | 3.98910 | + | 0.170194i | 0.364153 | + | 0.0155365i | ||||
\(121\) | 9.85165 | 0.895604 | ||||||||
\(122\) | − | 0.133657i | − | 0.0121007i | ||||||
\(123\) | 9.99734 | + | 0.426534i | 0.901430 | + | 0.0384593i | ||||
\(124\) | 1.81032i | 0.162572i | ||||||||
\(125\) | − | 10.8023i | − | 0.966185i | ||||||
\(126\) | 9.72175 | + | 0.831066i | 0.866083 | + | 0.0740372i | ||||
\(127\) | −3.14080 | −0.278701 | −0.139350 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139350 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −19.9864 | − | 0.852717i | −1.75971 | − | 0.0750775i | ||||
\(130\) | 5.63383 | 0.494120 | ||||||||
\(131\) | 10.9596 | 0.957541 | 0.478771 | − | 0.877940i | \(-0.341083\pi\) | ||||
0.478771 | + | 0.877940i | \(0.341083\pi\) | |||||||
\(132\) | 0.337136 | − | 7.90198i | 0.0293439 | − | 0.687779i | ||||
\(133\) | −4.27352 | −0.370561 | ||||||||
\(134\) | 3.33360i | 0.287979i | ||||||||
\(135\) | 11.8803 | + | 1.52803i | 1.02249 | + | 0.131512i | ||||
\(136\) | − | 2.52929i | − | 0.216885i | ||||||
\(137\) | − | 13.7212i | − | 1.17228i | −0.810209 | − | 0.586141i | \(-0.800646\pi\) | ||
0.810209 | − | 0.586141i | \(-0.199354\pi\) | |||||||
\(138\) | 0.624491 | − | 14.6371i | 0.0531602 | − | 1.24600i | ||||
\(139\) | −20.5507 | −1.74309 | −0.871545 | − | 0.490315i | \(-0.836882\pi\) | ||||
−0.871545 | + | 0.490315i | \(0.836882\pi\) | |||||||
\(140\) | − | 7.49745i | − | 0.633650i | ||||||
\(141\) | 0.0497818 | − | 1.16681i | 0.00419238 | − | 0.0982633i | ||||
\(142\) | − | 6.35743i | − | 0.533503i | ||||||
\(143\) | − | 11.1600i | − | 0.933248i | ||||||
\(144\) | −2.98910 | − | 0.255524i | −0.249092 | − | 0.0212936i | ||||
\(145\) | −17.4798 | −1.45162 | ||||||||
\(146\) | − | 13.4703i | − | 1.11481i | ||||||
\(147\) | 0.264175 | − | 6.19187i | 0.0217888 | − | 0.510697i | ||||
\(148\) | 2.83361i | 0.232921i | ||||||||
\(149\) | 17.0984 | 1.40076 | 0.700378 | − | 0.713772i | \(-0.253015\pi\) | ||||
0.700378 | + | 0.713772i | \(0.253015\pi\) | |||||||
\(150\) | 0.0231795 | − | 0.543295i | 0.00189260 | − | 0.0443598i | ||||
\(151\) | − | 13.9649i | − | 1.13644i | −0.822875 | − | 0.568222i | \(-0.807631\pi\) | ||
0.822875 | − | 0.568222i | \(-0.192369\pi\) | |||||||
\(152\) | 1.31396 | 0.106576 | ||||||||
\(153\) | 0.646294 | − | 7.56031i | 0.0522498 | − | 0.611215i | ||||
\(154\) | −14.8516 | −1.19678 | ||||||||
\(155\) | 4.17316 | 0.335196 | ||||||||
\(156\) | −4.22922 | − | 0.180439i | −0.338609 | − | 0.0144467i | ||||
\(157\) | − | 12.3655i | − | 0.986872i | −0.869782 | − | 0.493436i | \(-0.835741\pi\) | ||
0.869782 | − | 0.493436i | \(-0.164259\pi\) | |||||||
\(158\) | −11.0366 | −0.878023 | ||||||||
\(159\) | 14.2266 | + | 0.606973i | 1.12824 | + | 0.0481361i | ||||
\(160\) | 2.30520i | 0.182242i | ||||||||
\(161\) | −27.5103 | −2.16811 | ||||||||
\(162\) | −8.86942 | − | 1.52757i | −0.696847 | − | 0.120017i | ||||
\(163\) | −2.07360 | −0.162417 | −0.0812083 | − | 0.996697i | \(-0.525878\pi\) | ||||
−0.0812083 | + | 0.996697i | \(0.525878\pi\) | |||||||
\(164\) | 5.77722i | 0.451125i | ||||||||
\(165\) | −18.2157 | − | 0.777167i | −1.41809 | − | 0.0605024i | ||||
\(166\) | 9.52592 | 0.739355 | ||||||||
\(167\) | − | 17.7195i | − | 1.37118i | −0.727989 | − | 0.685589i | \(-0.759545\pi\) | ||
0.727989 | − | 0.685589i | \(-0.240455\pi\) | |||||||
\(168\) | −0.240126 | + | 5.62821i | −0.0185261 | + | 0.434226i | ||||
\(169\) | 7.02703 | 0.540541 | ||||||||
\(170\) | −5.83054 | −0.447182 | ||||||||
\(171\) | 3.92755 | + | 0.335747i | 0.300347 | + | 0.0256752i | ||||
\(172\) | − | 11.5497i | − | 0.880654i | ||||||
\(173\) | 1.06747 | 0.0811585 | 0.0405792 | − | 0.999176i | \(-0.487080\pi\) | ||||
0.0405792 | + | 0.999176i | \(0.487080\pi\) | |||||||
\(174\) | 13.1218 | + | 0.559839i | 0.994763 | + | 0.0424413i | ||||
\(175\) | −1.02111 | −0.0771890 | ||||||||
\(176\) | 4.56636 | 0.344202 | ||||||||
\(177\) | 3.29165 | − | 12.8905i | 0.247415 | − | 0.968910i | ||||
\(178\) | −4.28529 | −0.321196 | ||||||||
\(179\) | 12.6586 | 0.946151 | 0.473076 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473076 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(180\) | −0.589033 | + | 6.89048i | −0.0439040 | + | 0.513586i | ||||
\(181\) | 12.2036 | 0.907088 | 0.453544 | − | 0.891234i | \(-0.350160\pi\) | ||||
0.453544 | + | 0.891234i | \(0.350160\pi\) | |||||||
\(182\) | 7.94876i | 0.589201i | ||||||||
\(183\) | 0.231290 | + | 0.00986794i | 0.0170975 | + | 0.000729459i | ||||
\(184\) | 8.45845 | 0.623565 | ||||||||
\(185\) | 6.53205 | 0.480246 | ||||||||
\(186\) | −3.13272 | − | 0.133657i | −0.229702 | − | 0.00980020i | ||||
\(187\) | 11.5497i | 0.844596i | ||||||||
\(188\) | 0.674272 | 0.0491764 | ||||||||
\(189\) | −2.15590 | + | 16.7619i | −0.156819 | + | 1.21925i | ||||
\(190\) | − | 3.02894i | − | 0.219742i | ||||||
\(191\) | −17.4916 | −1.26565 | −0.632824 | − | 0.774296i | \(-0.718104\pi\) | ||||
−0.632824 | + | 0.774296i | \(0.718104\pi\) | |||||||
\(192\) | 0.0738304 | − | 1.73048i | 0.00532825 | − | 0.124886i | ||||
\(193\) | 3.92668 | 0.282648 | 0.141324 | − | 0.989963i | \(-0.454864\pi\) | ||||
0.141324 | + | 0.989963i | \(0.454864\pi\) | |||||||
\(194\) | − | 8.58240i | − | 0.616181i | ||||||
\(195\) | −0.415948 | + | 9.74922i | −0.0297867 | + | 0.698156i | ||||
\(196\) | 3.57813 | 0.255581 | ||||||||
\(197\) | 1.63966i | 0.116821i | 0.998293 | + | 0.0584106i | \(0.0186033\pi\) | ||||
−0.998293 | + | 0.0584106i | \(0.981397\pi\) | |||||||
\(198\) | 13.6493 | + | 1.16681i | 0.970014 | + | 0.0829218i | ||||
\(199\) | −20.5203 | −1.45464 | −0.727322 | − | 0.686297i | \(-0.759235\pi\) | ||||
−0.727322 | + | 0.686297i | \(0.759235\pi\) | |||||||
\(200\) | 0.313957 | 0.0222001 | ||||||||
\(201\) | −5.76871 | − | 0.246121i | −0.406893 | − | 0.0173600i | ||||
\(202\) | −8.85165 | −0.622800 | ||||||||
\(203\) | − | 24.6623i | − | 1.73095i | ||||||
\(204\) | 4.37689 | + | 0.186739i | 0.306443 | + | 0.0130743i | ||||
\(205\) | 13.3177 | 0.930145 | ||||||||
\(206\) | 13.6040i | 0.947835i | ||||||||
\(207\) | 25.2831 | + | 2.16133i | 1.75730 | + | 0.150223i | ||||
\(208\) | − | 2.44397i | − | 0.169458i | ||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 12.9742 | + | 0.553540i | 0.895302 | + | 0.0381979i | ||||
\(211\) | 17.9919i | 1.23862i | 0.785148 | + | 0.619308i | \(0.212587\pi\) | ||||
−0.785148 | + | 0.619308i | \(0.787413\pi\) | |||||||
\(212\) | 8.22118i | 0.564633i | ||||||||
\(213\) | 11.0014 | + | 0.469371i | 0.753802 | + | 0.0321608i | ||||
\(214\) | − | 11.2988i | − | 0.772369i | ||||||
\(215\) | −26.6243 | −1.81576 | ||||||||
\(216\) | 0.662864 | − | 5.15370i | 0.0451022 | − | 0.350665i | ||||
\(217\) | 5.88790i | 0.399697i | ||||||||
\(218\) | − | 19.2424i | − | 1.30326i | ||||||
\(219\) | 23.3101 | + | 0.994520i | 1.57515 | + | 0.0672034i | ||||
\(220\) | − | 10.5264i | − | 0.709689i | ||||||
\(221\) | 6.18151 | 0.415813 | ||||||||
\(222\) | −4.90350 | − | 0.209207i | −0.329101 | − | 0.0140410i | ||||
\(223\) | 12.8745 | 0.862138 | 0.431069 | − | 0.902319i | \(-0.358137\pi\) | ||||
0.431069 | + | 0.902319i | \(0.358137\pi\) | |||||||
\(224\) | −3.25240 | −0.217310 | ||||||||
\(225\) | 0.938447 | + | 0.0802233i | 0.0625632 | + | 0.00534822i | ||||
\(226\) | −9.70743 | −0.645729 | ||||||||
\(227\) | −6.85578 | −0.455034 | −0.227517 | − | 0.973774i | \(-0.573061\pi\) | ||||
−0.227517 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(228\) | −0.0970099 | + | 2.27377i | −0.00642464 | + | 0.150584i | ||||
\(229\) | 19.9984i | 1.32153i | 0.750592 | + | 0.660766i | \(0.229769\pi\) | ||||
−0.750592 | + | 0.660766i | \(0.770231\pi\) | |||||||
\(230\) | − | 19.4984i | − | 1.28569i | ||||||
\(231\) | 1.09650 | − | 25.7004i | 0.0721446 | − | 1.69096i | ||||
\(232\) | 7.58278i | 0.497834i | ||||||||
\(233\) | 3.71058 | 0.243088 | 0.121544 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121544 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(234\) | 0.624491 | − | 7.30525i | 0.0408242 | − | 0.477559i | ||||
\(235\) | − | 1.55433i | − | 0.101394i | ||||||
\(236\) | 7.51658 | + | 1.58147i | 0.489288 | + | 0.102945i | ||||
\(237\) | 0.814835 | − | 19.0985i | 0.0529292 | − | 1.24058i | ||||
\(238\) | − | 8.22629i | − | 0.533231i | ||||||
\(239\) | 27.3300i | 1.76783i | 0.467649 | + | 0.883914i | \(0.345101\pi\) | ||||
−0.467649 | + | 0.883914i | \(0.654899\pi\) | |||||||
\(240\) | −3.98910 | − | 0.170194i | −0.257495 | − | 0.0109860i | ||||
\(241\) | −20.6469 | −1.32998 | −0.664991 | − | 0.746851i | \(-0.731565\pi\) | ||||
−0.664991 | + | 0.746851i | \(0.731565\pi\) | |||||||
\(242\) | −9.85165 | −0.633288 | ||||||||
\(243\) | 3.29826 | − | 15.2355i | 0.211583 | − | 0.977360i | ||||
\(244\) | 0.133657i | 0.00855650i | ||||||||
\(245\) | − | 8.24832i | − | 0.526966i | ||||||
\(246\) | −9.99734 | − | 0.426534i | −0.637407 | − | 0.0271948i | ||||
\(247\) | 3.21126i | 0.204328i | ||||||||
\(248\) | − | 1.81032i | − | 0.114956i | ||||||
\(249\) | −0.703303 | + | 16.4844i | −0.0445700 | + | 1.04466i | ||||
\(250\) | 10.8023i | 0.683196i | ||||||||
\(251\) | 8.11629i | 0.512296i | 0.966638 | + | 0.256148i | \(0.0824534\pi\) | ||||
−0.966638 | + | 0.256148i | \(0.917547\pi\) | |||||||
\(252\) | −9.72175 | − | 0.831066i | −0.612413 | − | 0.0523522i | ||||
\(253\) | −38.6243 | −2.42829 | ||||||||
\(254\) | 3.14080 | 0.197071 | ||||||||
\(255\) | 0.430471 | − | 10.0896i | 0.0269571 | − | 0.631836i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.73061i | 0.295087i | 0.989056 | + | 0.147544i | \(0.0471367\pi\) | ||||
−0.989056 | + | 0.147544i | \(0.952863\pi\) | |||||||
\(258\) | 19.9864 | + | 0.852717i | 1.24430 | + | 0.0530878i | ||||
\(259\) | 9.21605i | 0.572657i | ||||||||
\(260\) | −5.63383 | −0.349396 | ||||||||
\(261\) | −1.93758 | + | 22.6657i | −0.119933 | + | 1.40297i | ||||
\(262\) | −10.9596 | −0.677084 | ||||||||
\(263\) | − | 21.4373i | − | 1.32188i | −0.750438 | − | 0.660941i | \(-0.770158\pi\) | ||
0.750438 | − | 0.660941i | \(-0.229842\pi\) | |||||||
\(264\) | −0.337136 | + | 7.90198i | −0.0207493 | + | 0.486333i | ||||
\(265\) | 18.9515 | 1.16418 | ||||||||
\(266\) | 4.27352 | 0.262026 | ||||||||
\(267\) | 0.316385 | − | 7.41559i | 0.0193624 | − | 0.453827i | ||||
\(268\) | − | 3.33360i | − | 0.203632i | ||||||
\(269\) | −10.2002 | −0.621917 | −0.310958 | − | 0.950424i | \(-0.600650\pi\) | ||||
−0.310958 | + | 0.950424i | \(0.600650\pi\) | |||||||
\(270\) | −11.8803 | − | 1.52803i | −0.723013 | − | 0.0929932i | ||||
\(271\) | −18.6667 | −1.13392 | −0.566961 | − | 0.823745i | \(-0.691881\pi\) | ||||
−0.566961 | + | 0.823745i | \(0.691881\pi\) | |||||||
\(272\) | 2.52929i | 0.153361i | ||||||||
\(273\) | −13.7551 | − | 0.586860i | −0.832499 | − | 0.0355184i | ||||
\(274\) | 13.7212i | 0.828929i | ||||||||
\(275\) | −1.43364 | −0.0864517 | ||||||||
\(276\) | −0.624491 | + | 14.6371i | −0.0375899 | + | 0.881053i | ||||
\(277\) | −16.7548 | −1.00670 | −0.503349 | − | 0.864083i | \(-0.667899\pi\) | ||||
−0.503349 | + | 0.864083i | \(0.667899\pi\) | |||||||
\(278\) | 20.5507 | 1.23255 | ||||||||
\(279\) | 0.462580 | − | 5.41123i | 0.0276939 | − | 0.323962i | ||||
\(280\) | 7.49745i | 0.448058i | ||||||||
\(281\) | 20.1007i | 1.19911i | 0.800335 | + | 0.599553i | \(0.204655\pi\) | ||||
−0.800335 | + | 0.599553i | \(0.795345\pi\) | |||||||
\(282\) | −0.0497818 | + | 1.16681i | −0.00296446 | + | 0.0694827i | ||||
\(283\) | 16.1703i | 0.961224i | 0.876933 | + | 0.480612i | \(0.159585\pi\) | ||||
−0.876933 | + | 0.480612i | \(0.840415\pi\) | |||||||
\(284\) | 6.35743i | 0.377244i | ||||||||
\(285\) | 5.24150 | + | 0.223628i | 0.310480 | + | 0.0132466i | ||||
\(286\) | 11.1600i | 0.659906i | ||||||||
\(287\) | 18.7898i | 1.10913i | ||||||||
\(288\) | 2.98910 | + | 0.255524i | 0.176134 | + | 0.0150569i | ||||
\(289\) | 10.6027 | 0.623686 | ||||||||
\(290\) | 17.4798 | 1.02645 | ||||||||
\(291\) | 14.8516 | + | 0.633642i | 0.870619 | + | 0.0371448i | ||||
\(292\) | 13.4703i | 0.788292i | ||||||||
\(293\) | − | 13.7092i | − | 0.800901i | −0.916318 | − | 0.400451i | \(-0.868854\pi\) | ||
0.916318 | − | 0.400451i | \(-0.131146\pi\) | |||||||
\(294\) | −0.264175 | + | 6.19187i | −0.0154070 | + | 0.361117i | ||||
\(295\) | 3.64560 | − | 17.3272i | 0.212255 | − | 1.00883i | ||||
\(296\) | − | 2.83361i | − | 0.164700i | ||||||
\(297\) | −3.02688 | + | 23.5336i | −0.175637 | + | 1.36556i | ||||
\(298\) | −17.0984 | −0.990484 | ||||||||
\(299\) | 20.6722i | 1.19550i | ||||||||
\(300\) | −0.0231795 | + | 0.543295i | −0.00133827 | + | 0.0313671i | ||||
\(301\) | − | 37.5642i | − | 2.16516i | ||||||
\(302\) | 13.9649i | 0.803588i | ||||||||
\(303\) | 0.653521 | − | 15.3176i | 0.0375438 | − | 0.879972i | ||||
\(304\) | −1.31396 | −0.0753606 | ||||||||
\(305\) | 0.308106 | 0.0176421 | ||||||||
\(306\) | −0.646294 | + | 7.56031i | −0.0369462 | + | 0.432194i | ||||
\(307\) | −4.75594 | −0.271436 | −0.135718 | − | 0.990748i | \(-0.543334\pi\) | ||||
−0.135718 | + | 0.990748i | \(0.543334\pi\) | |||||||
\(308\) | 14.8516 | 0.846251 | ||||||||
\(309\) | −23.5414 | − | 1.00439i | −1.33922 | − | 0.0571376i | ||||
\(310\) | −4.17316 | −0.237020 | ||||||||
\(311\) | 5.88211i | 0.333544i | 0.985996 | + | 0.166772i | \(0.0533343\pi\) | ||||
−0.985996 | + | 0.166772i | \(0.946666\pi\) | |||||||
\(312\) | 4.22922 | + | 0.180439i | 0.239433 | + | 0.0102153i | ||||
\(313\) | − | 1.28702i | − | 0.0727467i | −0.999338 | − | 0.0363733i | \(-0.988419\pi\) | ||
0.999338 | − | 0.0363733i | \(-0.0115806\pi\) | |||||||
\(314\) | 12.3655i | 0.697824i | ||||||||
\(315\) | −1.91577 | + | 22.4106i | −0.107942 | + | 1.26269i | ||||
\(316\) | 11.0366 | 0.620856 | ||||||||
\(317\) | 26.3959i | 1.48254i | 0.671205 | + | 0.741272i | \(0.265777\pi\) | ||||
−0.671205 | + | 0.741272i | \(0.734223\pi\) | |||||||
\(318\) | −14.2266 | − | 0.606973i | −0.797786 | − | 0.0340374i | ||||
\(319\) | − | 34.6257i | − | 1.93867i | ||||||
\(320\) | − | 2.30520i | − | 0.128865i | ||||||
\(321\) | 19.5523 | + | 0.834194i | 1.09130 | + | 0.0465602i | ||||
\(322\) | 27.5103 | 1.53309 | ||||||||
\(323\) | − | 3.32338i | − | 0.184918i | ||||||
\(324\) | 8.86942 | + | 1.52757i | 0.492745 | + | 0.0848650i | ||||
\(325\) | 0.767299i | 0.0425621i | ||||||||
\(326\) | 2.07360 | 0.114846 | ||||||||
\(327\) | 33.2986 | + | 1.42068i | 1.84142 | + | 0.0785636i | ||||
\(328\) | − | 5.77722i | − | 0.318993i | ||||||
\(329\) | 2.19301 | 0.120904 | ||||||||
\(330\) | 18.2157 | + | 0.777167i | 1.00274 | + | 0.0427816i | ||||
\(331\) | 15.7151 | 0.863778 | 0.431889 | − | 0.901927i | \(-0.357847\pi\) | ||||
0.431889 | + | 0.901927i | \(0.357847\pi\) | |||||||
\(332\) | −9.52592 | −0.522803 | ||||||||
\(333\) | 0.724054 | − | 8.46994i | 0.0396779 | − | 0.464150i | ||||
\(334\) | 17.7195i | 0.969569i | ||||||||
\(335\) | −7.68461 | −0.419855 | ||||||||
\(336\) | 0.240126 | − | 5.62821i | 0.0131000 | − | 0.307044i | ||||
\(337\) | 14.1561i | 0.771130i | 0.922681 | + | 0.385565i | \(0.125993\pi\) | ||||
−0.922681 | + | 0.385565i | \(0.874007\pi\) | |||||||
\(338\) | −7.02703 | −0.382220 | ||||||||
\(339\) | 0.716703 | − | 16.7985i | 0.0389260 | − | 0.912368i | ||||
\(340\) | 5.83054 | 0.316205 | ||||||||
\(341\) | 8.26659i | 0.447661i | ||||||||
\(342\) | −3.92755 | − | 0.335747i | −0.212377 | − | 0.0181551i | ||||
\(343\) | −11.1293 | −0.600926 | ||||||||
\(344\) | 11.5497i | 0.622717i | ||||||||
\(345\) | 33.7416 | + | 1.43958i | 1.81659 | + | 0.0775042i | ||||
\(346\) | −1.06747 | −0.0573877 | ||||||||
\(347\) | −17.5880 | −0.944174 | −0.472087 | − | 0.881552i | \(-0.656499\pi\) | ||||
−0.472087 | + | 0.881552i | \(0.656499\pi\) | |||||||
\(348\) | −13.1218 | − | 0.559839i | −0.703403 | − | 0.0300105i | ||||
\(349\) | − | 7.43449i | − | 0.397959i | −0.980004 | − | 0.198980i | \(-0.936237\pi\) | ||
0.980004 | − | 0.198980i | \(-0.0637628\pi\) | |||||||
\(350\) | 1.02111 | 0.0545808 | ||||||||
\(351\) | 12.5955 | + | 1.62002i | 0.672296 | + | 0.0864701i | ||||
\(352\) | −4.56636 | −0.243388 | ||||||||
\(353\) | −7.10990 | −0.378422 | −0.189211 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189211 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(354\) | −3.29165 | + | 12.8905i | −0.174949 | + | 0.685123i | ||||
\(355\) | 14.6552 | 0.777815 | ||||||||
\(356\) | 4.28529 | 0.227120 | ||||||||
\(357\) | 14.2354 | + | 0.607350i | 0.753417 | + | 0.0321444i | ||||
\(358\) | −12.6586 | −0.669030 | ||||||||
\(359\) | − | 23.3922i | − | 1.23459i | −0.786731 | − | 0.617296i | \(-0.788228\pi\) | ||
0.786731 | − | 0.617296i | \(-0.211772\pi\) | |||||||
\(360\) | 0.589033 | − | 6.89048i | 0.0310448 | − | 0.363160i | ||||
\(361\) | −17.2735 | −0.909133 | ||||||||
\(362\) | −12.2036 | −0.641408 | ||||||||
\(363\) | 0.727351 | − | 17.0480i | 0.0381760 | − | 0.894790i | ||||
\(364\) | − | 7.94876i | − | 0.416628i | ||||||
\(365\) | 31.0518 | 1.62533 | ||||||||
\(366\) | −0.231290 | − | 0.00986794i | −0.0120897 | − | 0.000515805i | ||||
\(367\) | 5.80088i | 0.302803i | 0.988472 | + | 0.151402i | \(0.0483787\pi\) | ||||
−0.988472 | + | 0.151402i | \(0.951621\pi\) | |||||||
\(368\) | −8.45845 | −0.440927 | ||||||||
\(369\) | 1.47621 | − | 17.2687i | 0.0768487 | − | 0.898971i | ||||
\(370\) | −6.53205 | −0.339585 | ||||||||
\(371\) | 26.7386i | 1.38820i | ||||||||
\(372\) | 3.13272 | + | 0.133657i | 0.162424 | + | 0.00692979i | ||||
\(373\) | 10.9210 | 0.565469 | 0.282735 | − | 0.959198i | \(-0.408758\pi\) | ||||
0.282735 | + | 0.959198i | \(0.408758\pi\) | |||||||
\(374\) | − | 11.5497i | − | 0.597219i | ||||||
\(375\) | −18.6931 | − | 0.797536i | −0.965307 | − | 0.0411846i | ||||
\(376\) | −0.674272 | −0.0347729 | ||||||||
\(377\) | −18.5320 | −0.954449 | ||||||||
\(378\) | 2.15590 | − | 16.7619i | 0.110888 | − | 0.862140i | ||||
\(379\) | 35.6952 | 1.83354 | 0.916770 | − | 0.399415i | \(-0.130787\pi\) | ||||
0.916770 | + | 0.399415i | \(0.130787\pi\) | |||||||
\(380\) | 3.02894i | 0.155381i | ||||||||
\(381\) | −0.231886 | + | 5.43507i | −0.0118799 | + | 0.278447i | ||||
\(382\) | 17.4916 | 0.894948 | ||||||||
\(383\) | 20.9229i | 1.06911i | 0.845134 | + | 0.534554i | \(0.179521\pi\) | ||||
−0.845134 | + | 0.534554i | \(0.820479\pi\) | |||||||
\(384\) | −0.0738304 | + | 1.73048i | −0.00376764 | + | 0.0883080i | ||||
\(385\) | − | 34.2361i | − | 1.74483i | ||||||
\(386\) | −3.92668 | −0.199863 | ||||||||
\(387\) | −2.95121 | + | 34.5231i | −0.150019 | + | 1.75491i | ||||
\(388\) | 8.58240i | 0.435706i | ||||||||
\(389\) | − | 1.93248i | − | 0.0979805i | −0.998799 | − | 0.0489903i | \(-0.984400\pi\) | ||
0.998799 | − | 0.0489903i | \(-0.0156003\pi\) | |||||||
\(390\) | 0.415948 | − | 9.74922i | 0.0210624 | − | 0.493671i | ||||
\(391\) | − | 21.3939i | − | 1.08194i | ||||||
\(392\) | −3.57813 | −0.180723 | ||||||||
\(393\) | 0.809149 | − | 18.9653i | 0.0408162 | − | 0.956671i | ||||
\(394\) | − | 1.63966i | − | 0.0826051i | ||||||
\(395\) | − | 25.4415i | − | 1.28010i | ||||||
\(396\) | −13.6493 | − | 1.16681i | −0.685903 | − | 0.0586345i | ||||
\(397\) | − | 19.2875i | − | 0.968012i | −0.875065 | − | 0.484006i | \(-0.839181\pi\) | ||
0.875065 | − | 0.484006i | \(-0.160819\pi\) | |||||||
\(398\) | 20.5203 | 1.02859 | ||||||||
\(399\) | −0.315516 | + | 7.39522i | −0.0157955 | + | 0.370224i | ||||
\(400\) | −0.313957 | −0.0156978 | ||||||||
\(401\) | 4.84743 | 0.242069 | 0.121035 | − | 0.992648i | \(-0.461379\pi\) | ||||
0.121035 | + | 0.992648i | \(0.461379\pi\) | |||||||
\(402\) | 5.76871 | + | 0.246121i | 0.287717 | + | 0.0122754i | ||||
\(403\) | 4.42437 | 0.220393 | ||||||||
\(404\) | 8.85165 | 0.440386 | ||||||||
\(405\) | 3.52136 | − | 20.4458i | 0.174978 | − | 1.01596i | ||||
\(406\) | 24.6623i | 1.22397i | ||||||||
\(407\) | 12.9393i | 0.641377i | ||||||||
\(408\) | −4.37689 | − | 0.186739i | −0.216688 | − | 0.00924495i | ||||
\(409\) | 36.9306i | 1.82610i | 0.407849 | + | 0.913049i | \(0.366279\pi\) | ||||
−0.407849 | + | 0.913049i | \(0.633721\pi\) | |||||||
\(410\) | −13.3177 | −0.657712 | ||||||||
\(411\) | −23.7442 | − | 1.01304i | −1.17122 | − | 0.0499697i | ||||
\(412\) | − | 13.6040i | − | 0.670221i | ||||||
\(413\) | 24.4470 | + | 5.14357i | 1.20296 | + | 0.253099i | ||||
\(414\) | −25.2831 | − | 2.16133i | −1.24260 | − | 0.106224i | ||||
\(415\) | 21.9592i | 1.07793i | ||||||||
\(416\) | 2.44397i | 0.119825i | ||||||||
\(417\) | −1.51727 | + | 35.5626i | −0.0743010 | + | 1.74151i | ||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −24.1961 | −1.18206 | −0.591028 | − | 0.806651i | \(-0.701278\pi\) | ||||
−0.591028 | + | 0.806651i | \(0.701278\pi\) | |||||||
\(420\) | −12.9742 | − | 0.553540i | −0.633074 | − | 0.0270100i | ||||
\(421\) | − | 23.5993i | − | 1.15016i | −0.818097 | − | 0.575080i | \(-0.804971\pi\) | ||
0.818097 | − | 0.575080i | \(-0.195029\pi\) | |||||||
\(422\) | − | 17.9919i | − | 0.875834i | ||||||
\(423\) | −2.01547 | − | 0.172292i | −0.0979953 | − | 0.00837715i | ||||
\(424\) | − | 8.22118i | − | 0.399256i | ||||||
\(425\) | − | 0.794089i | − | 0.0385190i | ||||||
\(426\) | −11.0014 | − | 0.469371i | −0.533018 | − | 0.0227411i | ||||
\(427\) | 0.434706i | 0.0210369i | ||||||||
\(428\) | 11.2988i | 0.546148i | ||||||||
\(429\) | −19.3122 | − | 0.823949i | −0.932400 | − | 0.0397806i | ||||
\(430\) | 26.6243 | 1.28394 | ||||||||
\(431\) | 30.4771 | 1.46803 | 0.734016 | − | 0.679132i | \(-0.237644\pi\) | ||||
0.734016 | + | 0.679132i | \(0.237644\pi\) | |||||||
\(432\) | −0.662864 | + | 5.15370i | −0.0318920 | + | 0.247957i | ||||
\(433\) | −37.7340 | −1.81338 | −0.906689 | − | 0.421799i | \(-0.861399\pi\) | ||||
−0.906689 | + | 0.421799i | \(0.861399\pi\) | |||||||
\(434\) | − | 5.88790i | − | 0.282628i | ||||||
\(435\) | −1.29054 | + | 30.2484i | −0.0618768 | + | 1.45030i | ||||
\(436\) | 19.2424i | 0.921546i | ||||||||
\(437\) | 11.1140 | 0.531656 | ||||||||
\(438\) | −23.3101 | − | 0.994520i | −1.11380 | − | 0.0475200i | ||||
\(439\) | −6.37650 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(440\) | 10.5264i | 0.501826i | ||||||||
\(441\) | −10.6954 | − | 0.914297i | −0.509304 | − | 0.0435379i | ||||
\(442\) | −6.18151 | −0.294024 | ||||||||
\(443\) | −21.9885 | −1.04471 | −0.522353 | − | 0.852730i | \(-0.674946\pi\) | ||||
−0.522353 | + | 0.852730i | \(0.674946\pi\) | |||||||
\(444\) | 4.90350 | + | 0.209207i | 0.232710 | + | 0.00992851i | ||||
\(445\) | − | 9.87846i | − | 0.468284i | ||||||
\(446\) | −12.8745 | −0.609624 | ||||||||
\(447\) | 1.26238 | − | 29.5884i | 0.0597086 | − | 1.39948i | ||||
\(448\) | 3.25240 | 0.153662 | ||||||||
\(449\) | − | 23.7841i | − | 1.12244i | −0.827666 | − | 0.561221i | \(-0.810332\pi\) | ||
0.827666 | − | 0.561221i | \(-0.189668\pi\) | |||||||
\(450\) | −0.938447 | − | 0.0802233i | −0.0442388 | − | 0.00378176i | ||||
\(451\) | 26.3809i | 1.24223i | ||||||||
\(452\) | 9.70743 | 0.456599 | ||||||||
\(453\) | −24.1659 | − | 1.03103i | −1.13541 | − | 0.0484421i | ||||
\(454\) | 6.85578 | 0.321758 | ||||||||
\(455\) | −18.3235 | −0.859019 | ||||||||
\(456\) | 0.0970099 | − | 2.27377i | 0.00454291 | − | 0.106479i | ||||
\(457\) | 8.86945i | 0.414896i | 0.978246 | + | 0.207448i | \(0.0665157\pi\) | ||||
−0.978246 | + | 0.207448i | \(0.933484\pi\) | |||||||
\(458\) | − | 19.9984i | − | 0.934465i | ||||||
\(459\) | −13.0352 | − | 1.67658i | −0.608432 | − | 0.0782560i | ||||
\(460\) | 19.4984i | 0.909119i | ||||||||
\(461\) | − | 17.7652i | − | 0.827408i | −0.910411 | − | 0.413704i | \(-0.864235\pi\) | ||
0.910411 | − | 0.413704i | \(-0.135765\pi\) | |||||||
\(462\) | −1.09650 | + | 25.7004i | −0.0510139 | + | 1.19569i | ||||
\(463\) | − | 27.7798i | − | 1.29104i | −0.763745 | − | 0.645518i | \(-0.776641\pi\) | ||
0.763745 | − | 0.645518i | \(-0.223359\pi\) | |||||||
\(464\) | − | 7.58278i | − | 0.352022i | ||||||
\(465\) | 0.308106 | − | 7.22156i | 0.0142881 | − | 0.334892i | ||||
\(466\) | −3.71058 | −0.171889 | ||||||||
\(467\) | 8.59729 | 0.397835 | 0.198918 | − | 0.980016i | \(-0.436257\pi\) | ||||
0.198918 | + | 0.980016i | \(0.436257\pi\) | |||||||
\(468\) | −0.624491 | + | 7.30525i | −0.0288671 | + | 0.337685i | ||||
\(469\) | − | 10.8422i | − | 0.500646i | ||||||
\(470\) | 1.55433i | 0.0716961i | ||||||||
\(471\) | −21.3982 | − | 0.912948i | −0.985975 | − | 0.0420664i | ||||
\(472\) | −7.51658 | − | 1.58147i | −0.345979 | − | 0.0727930i | ||||
\(473\) | − | 52.7400i | − | 2.42499i | ||||||
\(474\) | −0.814835 | + | 19.0985i | −0.0374266 | + | 0.877225i | ||||
\(475\) | 0.412525 | 0.0189280 | ||||||||
\(476\) | 8.22629i | 0.377051i | ||||||||
\(477\) | 2.10071 | − | 24.5739i | 0.0961847 | − | 1.12516i | ||||
\(478\) | − | 27.3300i | − | 1.25004i | ||||||
\(479\) | − | 33.5116i | − | 1.53119i | −0.643326 | − | 0.765593i | \(-0.722446\pi\) | ||
0.643326 | − | 0.765593i | \(-0.277554\pi\) | |||||||
\(480\) | 3.98910 | + | 0.170194i | 0.182077 | + | 0.00776826i | ||||
\(481\) | 6.92525 | 0.315764 | ||||||||
\(482\) | 20.6469 | 0.940439 | ||||||||
\(483\) | −2.03110 | + | 47.6059i | −0.0924181 | + | 2.16614i | ||||
\(484\) | 9.85165 | 0.447802 | ||||||||
\(485\) | 19.7842 | 0.898353 | ||||||||
\(486\) | −3.29826 | + | 15.2355i | −0.149612 | + | 0.691098i | ||||
\(487\) | 15.2524 | 0.691152 | 0.345576 | − | 0.938391i | \(-0.387683\pi\) | ||||
0.345576 | + | 0.938391i | \(0.387683\pi\) | |||||||
\(488\) | − | 0.133657i | − | 0.00605036i | ||||||
\(489\) | −0.153094 | + | 3.58831i | −0.00692317 | + | 0.162269i | ||||
\(490\) | 8.24832i | 0.372621i | ||||||||
\(491\) | − | 11.8006i | − | 0.532552i | −0.963897 | − | 0.266276i | \(-0.914207\pi\) | ||
0.963897 | − | 0.266276i | \(-0.0857932\pi\) | |||||||
\(492\) | 9.99734 | + | 0.426534i | 0.450715 | + | 0.0192296i | ||||
\(493\) | 19.1791 | 0.863782 | ||||||||
\(494\) | − | 3.21126i | − | 0.144482i | ||||||
\(495\) | −2.68974 | + | 31.4644i | −0.120895 | + | 1.41422i | ||||
\(496\) | 1.81032i | 0.0812859i | ||||||||
\(497\) | 20.6769i | 0.927486i | ||||||||
\(498\) | 0.703303 | − | 16.4844i | 0.0315157 | − | 0.738683i | ||||
\(499\) | −13.2132 | −0.591506 | −0.295753 | − | 0.955265i | \(-0.595570\pi\) | ||||
−0.295753 | + | 0.955265i | \(0.595570\pi\) | |||||||
\(500\) | − | 10.8023i | − | 0.483093i | ||||||
\(501\) | −30.6632 | − | 1.30824i | −1.36993 | − | 0.0584478i | ||||
\(502\) | − | 8.11629i | − | 0.362248i | ||||||
\(503\) | −10.2884 | −0.458739 | −0.229369 | − | 0.973339i | \(-0.573666\pi\) | ||||
−0.229369 | + | 0.973339i | \(0.573666\pi\) | |||||||
\(504\) | 9.72175 | + | 0.831066i | 0.433041 | + | 0.0370186i | ||||
\(505\) | − | 20.4048i | − | 0.908003i | ||||||
\(506\) | 38.6243 | 1.71706 | ||||||||
\(507\) | 0.518809 | − | 12.1601i | 0.0230411 | − | 0.540050i | ||||
\(508\) | −3.14080 | −0.139350 | ||||||||
\(509\) | −20.9356 | −0.927953 | −0.463977 | − | 0.885847i | \(-0.653578\pi\) | ||||
−0.463977 | + | 0.885847i | \(0.653578\pi\) | |||||||
\(510\) | −0.430471 | + | 10.0896i | −0.0190616 | + | 0.446775i | ||||
\(511\) | 43.8110i | 1.93808i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.870974 | − | 6.77174i | 0.0384545 | − | 0.298979i | ||||
\(514\) | − | 4.73061i | − | 0.208658i | ||||||
\(515\) | −31.3599 | −1.38188 | ||||||||
\(516\) | −19.9864 | − | 0.852717i | −0.879854 | − | 0.0375388i | ||||
\(517\) | 3.07897 | 0.135413 | ||||||||
\(518\) | − | 9.21605i | − | 0.404930i | ||||||
\(519\) | 0.0788120 | − | 1.84724i | 0.00345946 | − | 0.0810847i | ||||
\(520\) | 5.63383 | 0.247060 | ||||||||
\(521\) | 29.3907i | 1.28763i | 0.765181 | + | 0.643815i | \(0.222649\pi\) | ||||
−0.765181 | + | 0.643815i | \(0.777351\pi\) | |||||||
\(522\) | 1.93758 | − | 22.6657i | 0.0848055 | − | 0.992049i | ||||
\(523\) | −21.0950 | −0.922419 | −0.461210 | − | 0.887291i | \(-0.652584\pi\) | ||||
−0.461210 | + | 0.887291i | \(0.652584\pi\) | |||||||
\(524\) | 10.9596 | 0.478771 | ||||||||
\(525\) | −0.0753892 | + | 1.76701i | −0.00329026 | + | 0.0771188i | ||||
\(526\) | 21.4373i | 0.934711i | ||||||||
\(527\) | −4.57884 | −0.199457 | ||||||||
\(528\) | 0.337136 | − | 7.90198i | 0.0146720 | − | 0.343890i | ||||
\(529\) | 48.5454 | 2.11067 | ||||||||
\(530\) | −18.9515 | −0.823200 | ||||||||
\(531\) | −22.0637 | − | 6.64783i | −0.957483 | − | 0.288491i | ||||
\(532\) | −4.27352 | −0.185280 | ||||||||
\(533\) | 14.1193 | 0.611575 | ||||||||
\(534\) | −0.316385 | + | 7.41559i | −0.0136913 | + | 0.320904i | ||||
\(535\) | 26.0460 | 1.12607 | ||||||||
\(536\) | 3.33360i | 0.143989i | ||||||||
\(537\) | 0.934593 | − | 21.9055i | 0.0403306 | − | 0.945291i | ||||
\(538\) | 10.2002 | 0.439762 | ||||||||
\(539\) | 16.3390 | 0.703772 | ||||||||
\(540\) | 11.8803 | + | 1.52803i | 0.511247 | + | 0.0657562i | ||||
\(541\) | − | 11.6743i | − | 0.501917i | −0.967998 | − | 0.250959i | \(-0.919254\pi\) | ||
0.967998 | − | 0.250959i | \(-0.0807458\pi\) | |||||||
\(542\) | 18.6667 | 0.801804 | ||||||||
\(543\) | 0.900998 | − | 21.1181i | 0.0386655 | − | 0.906263i | ||||
\(544\) | − | 2.52929i | − | 0.108443i | ||||||
\(545\) | 44.3577 | 1.90008 | ||||||||
\(546\) | 13.7551 | + | 0.586860i | 0.588666 | + | 0.0251153i | ||||
\(547\) | 26.6015 | 1.13740 | 0.568699 | − | 0.822546i | \(-0.307447\pi\) | ||||
0.568699 | + | 0.822546i | \(0.307447\pi\) | |||||||
\(548\) | − | 13.7212i | − | 0.586141i | ||||||
\(549\) | 0.0341525 | − | 0.399513i | 0.00145759 | − | 0.0170508i | ||||
\(550\) | 1.43364 | 0.0611306 | ||||||||
\(551\) | 9.96344i | 0.424457i | ||||||||
\(552\) | 0.624491 | − | 14.6371i | 0.0265801 | − | 0.622998i | ||||
\(553\) | 35.8954 | 1.52643 | ||||||||
\(554\) | 16.7548 | 0.711843 | ||||||||
\(555\) | 0.482263 | − | 11.3036i | 0.0204709 | − | 0.479809i | ||||
\(556\) | −20.5507 | −0.871545 | ||||||||
\(557\) | − | 1.86705i | − | 0.0791096i | −0.999217 | − | 0.0395548i | \(-0.987406\pi\) | ||
0.999217 | − | 0.0395548i | \(-0.0125940\pi\) | |||||||
\(558\) | −0.462580 | + | 5.41123i | −0.0195826 | + | 0.229076i | ||||
\(559\) | −28.2270 | −1.19387 | ||||||||
\(560\) | − | 7.49745i | − | 0.316825i | ||||||
\(561\) | 19.9864 | + | 0.852717i | 0.843828 | + | 0.0360017i | ||||
\(562\) | − | 20.1007i | − | 0.847896i | ||||||
\(563\) | −31.9221 | −1.34536 | −0.672678 | − | 0.739935i | \(-0.734856\pi\) | ||||
−0.672678 | + | 0.739935i | \(0.734856\pi\) | |||||||
\(564\) | 0.0497818 | − | 1.16681i | 0.00209619 | − | 0.0491317i | ||||
\(565\) | − | 22.3776i | − | 0.941432i | ||||||
\(566\) | − | 16.1703i | − | 0.679688i | ||||||
\(567\) | 28.8469 | + | 4.96827i | 1.21146 | + | 0.208648i | ||||
\(568\) | − | 6.35743i | − | 0.266752i | ||||||
\(569\) | −14.8215 | −0.621348 | −0.310674 | − | 0.950517i | \(-0.600555\pi\) | ||||
−0.310674 | + | 0.950517i | \(0.600555\pi\) | |||||||
\(570\) | −5.24150 | − | 0.223628i | −0.219542 | − | 0.00936673i | ||||
\(571\) | 34.3763i | 1.43860i | 0.694699 | + | 0.719301i | \(0.255538\pi\) | ||||
−0.694699 | + | 0.719301i | \(0.744462\pi\) | |||||||
\(572\) | − | 11.1600i | − | 0.466624i | ||||||
\(573\) | −1.29141 | + | 30.2688i | −0.0539495 | + | 1.26450i | ||||
\(574\) | − | 18.7898i | − | 0.784273i | ||||||
\(575\) | 2.65559 | 0.110746 | ||||||||
\(576\) | −2.98910 | − | 0.255524i | −0.124546 | − | 0.0106468i | ||||
\(577\) | −16.7941 | −0.699146 | −0.349573 | − | 0.936909i | \(-0.613673\pi\) | ||||
−0.349573 | + | 0.936909i | \(0.613673\pi\) | |||||||
\(578\) | −10.6027 | −0.441013 | ||||||||
\(579\) | 0.289908 | − | 6.79502i | 0.0120482 | − | 0.282391i | ||||
\(580\) | −17.4798 | −0.725811 | ||||||||
\(581\) | −30.9821 | −1.28536 | ||||||||
\(582\) | −14.8516 | − | 0.633642i | −0.615621 | − | 0.0262653i | ||||
\(583\) | 37.5409i | 1.55478i | ||||||||
\(584\) | − | 13.4703i | − | 0.557406i | ||||||
\(585\) | 16.8401 | + | 1.43958i | 0.696252 | + | 0.0595192i | ||||
\(586\) | 13.7092i | 0.566323i | ||||||||
\(587\) | −33.8463 | −1.39699 | −0.698493 | − | 0.715617i | \(-0.746146\pi\) | ||||
−0.698493 | + | 0.715617i | \(0.746146\pi\) | |||||||
\(588\) | 0.264175 | − | 6.19187i | 0.0108944 | − | 0.255349i | ||||
\(589\) | − | 2.37869i | − | 0.0980120i | ||||||
\(590\) | −3.64560 | + | 17.3272i | −0.150087 | + | 0.713351i | ||||
\(591\) | 2.83740 | + | 0.121057i | 0.116715 | + | 0.00497962i | ||||
\(592\) | 2.83361i | 0.116461i | ||||||||
\(593\) | − | 13.8626i | − | 0.569269i | −0.958636 | − | 0.284635i | \(-0.908128\pi\) | ||
0.958636 | − | 0.284635i | \(-0.0918723\pi\) | |||||||
\(594\) | 3.02688 | − | 23.5336i | 0.124194 | − | 0.965597i | ||||
\(595\) | 18.9633 | 0.777418 | ||||||||
\(596\) | 17.0984 | 0.700378 | ||||||||
\(597\) | −1.51502 | + | 35.5099i | −0.0620056 | + | 1.45332i | ||||
\(598\) | − | 20.6722i | − | 0.845347i | ||||||
\(599\) | 3.89307i | 0.159066i | 0.996832 | + | 0.0795332i | \(0.0253430\pi\) | ||||
−0.996832 | + | 0.0795332i | \(0.974657\pi\) | |||||||
\(600\) | 0.0231795 | − | 0.543295i | 0.000946301 | − | 0.0221799i | ||||
\(601\) | 5.74105i | 0.234182i | 0.993121 | + | 0.117091i | \(0.0373570\pi\) | ||||
−0.993121 | + | 0.117091i | \(0.962643\pi\) | |||||||
\(602\) | 37.5642i | 1.53100i | ||||||||
\(603\) | −0.851812 | + | 9.96445i | −0.0346885 | + | 0.405784i | ||||
\(604\) | − | 13.9649i | − | 0.568222i | ||||||
\(605\) | − | 22.7100i | − | 0.923295i | ||||||
\(606\) | −0.653521 | + | 15.3176i | −0.0265475 | + | 0.622234i | ||||
\(607\) | −18.3429 | −0.744515 | −0.372258 | − | 0.928129i | \(-0.621416\pi\) | ||||
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(608\) | 1.31396 | 0.0532880 | ||||||||
\(609\) | −42.6775 | − | 1.82082i | −1.72938 | − | 0.0737835i | ||||
\(610\) | −0.308106 | −0.0124748 | ||||||||
\(611\) | − | 1.64790i | − | 0.0666668i | ||||||
\(612\) | 0.646294 | − | 7.56031i | 0.0261249 | − | 0.305607i | ||||
\(613\) | 43.0978i | 1.74070i | 0.492432 | + | 0.870351i | \(0.336108\pi\) | ||||
−0.492432 | + | 0.870351i | \(0.663892\pi\) | |||||||
\(614\) | 4.75594 | 0.191934 | ||||||||
\(615\) | 0.983248 | − | 23.0459i | 0.0396484 | − | 0.929300i | ||||
\(616\) | −14.8516 | −0.598390 | ||||||||
\(617\) | 15.0453i | 0.605703i | 0.953038 | + | 0.302851i | \(0.0979386\pi\) | ||||
−0.953038 | + | 0.302851i | \(0.902061\pi\) | |||||||
\(618\) | 23.5414 | + | 1.00439i | 0.946974 | + | 0.0404024i | ||||
\(619\) | 31.6765 | 1.27319 | 0.636594 | − | 0.771199i | \(-0.280343\pi\) | ||||
0.636594 | + | 0.771199i | \(0.280343\pi\) | |||||||
\(620\) | 4.17316 | 0.167598 | ||||||||
\(621\) | 5.60680 | − | 43.5923i | 0.224993 | − | 1.74930i | ||||
\(622\) | − | 5.88211i | − | 0.235851i | ||||||
\(623\) | 13.9375 | 0.558394 | ||||||||
\(624\) | −4.22922 | − | 0.180439i | −0.169304 | − | 0.00722334i | ||||
\(625\) | −26.4712 | −1.05885 | ||||||||
\(626\) | 1.28702i | 0.0514397i | ||||||||
\(627\) | −0.442982 | + | 10.3829i | −0.0176910 | + | 0.414651i | ||||
\(628\) | − | 12.3655i | − | 0.493436i | ||||||
\(629\) | −7.16704 | −0.285768 | ||||||||
\(630\) | 1.91577 | − | 22.4106i | 0.0763263 | − | 0.892860i | ||||
\(631\) | 6.52370 | 0.259704 | 0.129852 | − | 0.991533i | \(-0.458550\pi\) | ||||
0.129852 | + | 0.991533i | \(0.458550\pi\) | |||||||
\(632\) | −11.0366 | −0.439012 | ||||||||
\(633\) | 31.1346 | + | 1.32835i | 1.23749 | + | 0.0527972i | ||||
\(634\) | − | 26.3959i | − | 1.04832i | ||||||
\(635\) | 7.24017i | 0.287317i | ||||||||
\(636\) | 14.2266 | + | 0.606973i | 0.564120 | + | 0.0240680i | ||||
\(637\) | − | 8.74483i | − | 0.346483i | ||||||
\(638\) | 34.6257i | 1.37084i | ||||||||
\(639\) | 1.62447 | − | 19.0030i | 0.0642631 | − | 0.751746i | ||||
\(640\) | 2.30520i | 0.0911211i | ||||||||
\(641\) | 17.7734i | 0.702009i | 0.936374 | + | 0.351004i | \(0.114160\pi\) | ||||
−0.936374 | + | 0.351004i | \(0.885840\pi\) | |||||||
\(642\) | −19.5523 | − | 0.834194i | −0.771667 | − | 0.0329230i | ||||
\(643\) | 4.15400 | 0.163818 | 0.0819088 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819088 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(644\) | −27.5103 | −1.08406 | ||||||||
\(645\) | −1.96568 | + | 46.0728i | −0.0773988 | + | 1.81411i | ||||
\(646\) | 3.32338i | 0.130757i | ||||||||
\(647\) | − | 9.60059i | − | 0.377438i | −0.982031 | − | 0.188719i | \(-0.939566\pi\) | ||
0.982031 | − | 0.188719i | \(-0.0604335\pi\) | |||||||
\(648\) | −8.86942 | − | 1.52757i | −0.348424 | − | 0.0600086i | ||||
\(649\) | 34.3234 | + | 7.22156i | 1.34731 | + | 0.283471i | ||||
\(650\) | − | 0.767299i | − | 0.0300959i | ||||||
\(651\) | 10.1889 | + | 0.434706i | 0.399333 | + | 0.0170375i | ||||
\(652\) | −2.07360 | −0.0812083 | ||||||||
\(653\) | − | 0.316162i | − | 0.0123724i | −0.999981 | − | 0.00618618i | \(-0.998031\pi\) | ||
0.999981 | − | 0.00618618i | \(-0.00196914\pi\) | |||||||
\(654\) | −33.2986 | − | 1.42068i | −1.30208 | − | 0.0555529i | ||||
\(655\) | − | 25.2640i | − | 0.987146i | ||||||
\(656\) | 5.77722i | 0.225562i | ||||||||
\(657\) | 3.44199 | − | 40.2642i | 0.134285 | − | 1.57085i | ||||
\(658\) | −2.19301 | −0.0854923 | ||||||||
\(659\) | −14.2468 | −0.554975 | −0.277487 | − | 0.960729i | \(-0.589502\pi\) | ||||
−0.277487 | + | 0.960729i | \(0.589502\pi\) | |||||||
\(660\) | −18.2157 | − | 0.777167i | −0.709044 | − | 0.0302512i | ||||
\(661\) | −36.5390 | −1.42120 | −0.710600 | − | 0.703596i | \(-0.751577\pi\) | ||||
−0.710600 | + | 0.703596i | \(0.751577\pi\) | |||||||
\(662\) | −15.7151 | −0.610784 | ||||||||
\(663\) | 0.456383 | − | 10.6970i | 0.0177245 | − | 0.415435i | ||||
\(664\) | 9.52592 | 0.369677 | ||||||||
\(665\) | 9.85132i | 0.382018i | ||||||||
\(666\) | −0.724054 | + | 8.46994i | −0.0280565 | + | 0.328204i | ||||
\(667\) | 64.1385i | 2.48345i | ||||||||
\(668\) | − | 17.7195i | − | 0.685589i | ||||||
\(669\) | 0.950527 | − | 22.2790i | 0.0367495 | − | 0.861354i | ||||
\(670\) | 7.68461 | 0.296882 | ||||||||
\(671\) | 0.610325i | 0.0235614i | ||||||||
\(672\) | −0.240126 | + | 5.62821i | −0.00926307 | + | 0.217113i | ||||
\(673\) | − | 25.5961i | − | 0.986658i | −0.869843 | − | 0.493329i | \(-0.835780\pi\) | ||
0.869843 | − | 0.493329i | \(-0.164220\pi\) | |||||||
\(674\) | − | 14.1561i | − | 0.545271i | ||||||
\(675\) | 0.208111 | − | 1.61804i | 0.00801018 | − | 0.0622783i | ||||
\(676\) | 7.02703 | 0.270271 | ||||||||
\(677\) | − | 11.7568i | − | 0.451852i | −0.974144 | − | 0.225926i | \(-0.927459\pi\) | ||
0.974144 | − | 0.225926i | \(-0.0725408\pi\) | |||||||
\(678\) | −0.716703 | + | 16.7985i | −0.0275248 | + | 0.645142i | ||||
\(679\) | 27.9134i | 1.07122i | ||||||||
\(680\) | −5.83054 | −0.223591 | ||||||||
\(681\) | −0.506165 | + | 11.8638i | −0.0193963 | + | 0.454621i | ||||
\(682\) | − | 8.26659i | − | 0.316544i | ||||||
\(683\) | 45.3837 | 1.73656 | 0.868279 | − | 0.496075i | \(-0.165226\pi\) | ||||
0.868279 | + | 0.496075i | \(0.165226\pi\) | |||||||
\(684\) | 3.92755 | + | 0.335747i | 0.150173 | + | 0.0128376i | ||||
\(685\) | −31.6302 | −1.20853 | ||||||||
\(686\) | 11.1293 | 0.424919 | ||||||||
\(687\) | 34.6068 | + | 1.47649i | 1.32033 | + | 0.0563317i | ||||
\(688\) | − | 11.5497i | − | 0.440327i | ||||||
\(689\) | 20.0923 | 0.765455 | ||||||||
\(690\) | −33.7416 | − | 1.43958i | −1.28452 | − | 0.0548038i | ||||
\(691\) | − | 22.1246i | − | 0.841658i | −0.907140 | − | 0.420829i | \(-0.861739\pi\) | ||
0.907140 | − | 0.420829i | \(-0.138261\pi\) | |||||||
\(692\) | 1.06747 | 0.0405792 | ||||||||
\(693\) | −44.3930 | − | 3.79495i | −1.68635 | − | 0.144158i | ||||
\(694\) | 17.5880 | 0.667632 | ||||||||
\(695\) | 47.3736i | 1.79698i | ||||||||
\(696\) | 13.1218 | + | 0.559839i | 0.497381 | + | 0.0212207i | ||||
\(697\) | −14.6123 | −0.553480 | ||||||||
\(698\) | 7.43449i | 0.281400i | ||||||||
\(699\) | 0.273954 | − | 6.42107i | 0.0103619 | − | 0.242867i | ||||
\(700\) | −1.02111 | −0.0385945 | ||||||||
\(701\) | −22.4779 | −0.848978 | −0.424489 | − | 0.905433i | \(-0.639546\pi\) | ||||
−0.424489 | + | 0.905433i | \(0.639546\pi\) | |||||||
\(702\) | −12.5955 | − | 1.62002i | −0.475385 | − | 0.0611436i | ||||
\(703\) | − | 3.72324i | − | 0.140425i | ||||||
\(704\) | 4.56636 | 0.172101 | ||||||||
\(705\) | −2.68974 | − | 0.114757i | −0.101301 | − | 0.00432200i | ||||
\(706\) | 7.10990 | 0.267585 | ||||||||
\(707\) | 28.7891 | 1.08273 | ||||||||
\(708\) | 3.29165 | − | 12.8905i | 0.123708 | − | 0.484455i | ||||
\(709\) | 30.1704 | 1.13307 | 0.566536 | − | 0.824037i | \(-0.308283\pi\) | ||||
0.566536 | + | 0.824037i | \(0.308283\pi\) | |||||||
\(710\) | −14.6552 | −0.549998 | ||||||||
\(711\) | −32.9894 | − | 2.82011i | −1.23720 | − | 0.105762i | ||||
\(712\) | −4.28529 | −0.160598 | ||||||||
\(713\) | − | 15.3125i | − | 0.573459i | ||||||
\(714\) | −14.2354 | − | 0.607350i | −0.532746 | − | 0.0227295i | ||||
\(715\) | −25.7261 | −0.962102 | ||||||||
\(716\) | 12.6586 | 0.473076 | ||||||||
\(717\) | 47.2939 | + | 2.01778i | 1.76622 | + | 0.0753555i | ||||
\(718\) | 23.3922i | 0.872989i | ||||||||
\(719\) | 26.3466 | 0.982564 | 0.491282 | − | 0.871001i | \(-0.336528\pi\) | ||||
0.491282 | + | 0.871001i | \(0.336528\pi\) | |||||||
\(720\) | −0.589033 | + | 6.89048i | −0.0219520 | + | 0.256793i | ||||
\(721\) | − | 44.2457i | − | 1.64780i | ||||||
\(722\) | 17.2735 | 0.642854 | ||||||||
\(723\) | −1.52437 | + | 35.7289i | −0.0566918 | + | 1.32877i | ||||
\(724\) | 12.2036 | 0.453544 | ||||||||
\(725\) | 2.38066i | 0.0884156i | ||||||||
\(726\) | −0.727351 | + | 17.0480i | −0.0269945 | + | 0.632712i | ||||
\(727\) | 3.12553 | 0.115920 | 0.0579598 | − | 0.998319i | \(-0.481540\pi\) | ||||
0.0579598 | + | 0.998319i | \(0.481540\pi\) | |||||||
\(728\) | 7.94876i | 0.294601i | ||||||||
\(729\) | −26.1212 | − | 6.83240i | −0.967453 | − | 0.253052i | ||||
\(730\) | −31.0518 | −1.14928 | ||||||||
\(731\) | 29.2125 | 1.08046 | ||||||||
\(732\) | 0.231290 | + | 0.00986794i | 0.00854873 | + | 0.000364730i | ||||
\(733\) | 19.7033 | 0.727758 | 0.363879 | − | 0.931446i | \(-0.381452\pi\) | ||||
0.363879 | + | 0.931446i | \(0.381452\pi\) | |||||||
\(734\) | − | 5.80088i | − | 0.214114i | ||||||
\(735\) | −14.2735 | − | 0.608976i | −0.526487 | − | 0.0224624i | ||||
\(736\) | 8.45845 | 0.311783 | ||||||||
\(737\) | − | 15.2224i | − | 0.560724i | ||||||
\(738\) | −1.47621 | + | 17.2687i | −0.0543402 | + | 0.635668i | ||||
\(739\) | − | 40.8815i | − | 1.50385i | −0.659248 | − | 0.751925i | \(-0.729125\pi\) | ||
0.659248 | − | 0.751925i | \(-0.270875\pi\) | |||||||
\(740\) | 6.53205 | 0.240123 | ||||||||
\(741\) | 5.55702 | + | 0.237089i | 0.204142 | + | 0.00870968i | ||||
\(742\) | − | 26.7386i | − | 0.981605i | ||||||
\(743\) | − | 7.23882i | − | 0.265567i | −0.991145 | − | 0.132783i | \(-0.957609\pi\) | ||
0.991145 | − | 0.132783i | \(-0.0423914\pi\) | |||||||
\(744\) | −3.13272 | − | 0.133657i | −0.114851 | − | 0.00490010i | ||||
\(745\) | − | 39.4153i | − | 1.44406i | ||||||
\(746\) | −10.9210 | −0.399847 | ||||||||
\(747\) | 28.4739 | + | 2.43410i | 1.04181 | + | 0.0890590i | ||||
\(748\) | 11.5497i | 0.422298i | ||||||||
\(749\) | 36.7482i | 1.34275i | ||||||||
\(750\) | 18.6931 | + | 0.797536i | 0.682575 | + | 0.0291219i | ||||
\(751\) | − | 38.6007i | − | 1.40856i | −0.709923 | − | 0.704279i | \(-0.751270\pi\) | ||
0.709923 | − | 0.704279i | \(-0.248730\pi\) | |||||||
\(752\) | 0.674272 | 0.0245882 | ||||||||
\(753\) | 14.0451 | + | 0.599229i | 0.511830 | + | 0.0218371i | ||||
\(754\) | 18.5320 | 0.674897 | ||||||||
\(755\) | −32.1918 | −1.17158 | ||||||||
\(756\) | −2.15590 | + | 16.7619i | −0.0784094 | + | 0.609625i | ||||
\(757\) | 14.8860 | 0.541041 | 0.270521 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270521 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(758\) | −35.6952 | −1.29651 | ||||||||
\(759\) | −2.85165 | + | 66.8385i | −0.103508 | + | 2.42608i | ||||
\(760\) | − | 3.02894i | − | 0.109871i | ||||||
\(761\) | 38.9612i | 1.41234i | 0.708041 | + | 0.706171i | \(0.249579\pi\) | ||||
−0.708041 | + | 0.706171i | \(0.750421\pi\) | |||||||
\(762\) | 0.231886 | − | 5.43507i | 0.00840035 | − | 0.196892i | ||||
\(763\) | 62.5842i | 2.26570i | ||||||||
\(764\) | −17.4916 | −0.632824 | ||||||||
\(765\) | −17.4280 | − | 1.48984i | −0.630112 | − | 0.0538652i | ||||
\(766\) | − | 20.9229i | − | 0.755974i | ||||||
\(767\) | 3.86505 | − | 18.3703i | 0.139559 | − | 0.663312i | ||||
\(768\) | 0.0738304 | − | 1.73048i | 0.00266412 | − | 0.0624432i | ||||
\(769\) | 9.07465i | 0.327240i | 0.986523 | + | 0.163620i | \(0.0523171\pi\) | ||||
−0.986523 | + | 0.163620i | \(0.947683\pi\) | |||||||
\(770\) | 34.2361i | 1.23378i | ||||||||
\(771\) | 8.18621 | + | 0.349263i | 0.294819 | + | 0.0125784i | ||||
\(772\) | 3.92668 | 0.141324 | ||||||||
\(773\) | −6.98553 | −0.251252 | −0.125626 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125626 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(774\) | 2.95121 | − | 34.5231i | 0.106079 | − | 1.24091i | ||||
\(775\) | − | 0.568363i | − | 0.0204162i | ||||||
\(776\) | − | 8.58240i | − | 0.308090i | ||||||
\(777\) | 15.9482 | + | 0.680424i | 0.572137 | + | 0.0244101i | ||||
\(778\) | 1.93248i | 0.0692827i | ||||||||
\(779\) | − | 7.59101i | − | 0.271976i | ||||||
\(780\) | −0.415948 | + | 9.74922i | −0.0148933 | + | 0.349078i | ||||
\(781\) | 29.0303i | 1.03879i | ||||||||
\(782\) | 21.3939i | 0.765045i | ||||||||
\(783\) | 39.0794 | + | 5.02635i | 1.39658 | + | 0.179627i | ||||
\(784\) | 3.57813 | 0.127790 | ||||||||
\(785\) | −28.5049 | −1.01738 | ||||||||
\(786\) | −0.809149 | + | 18.9653i | −0.0288614 | + | 0.676469i | ||||
\(787\) | 12.5507 | 0.447385 | 0.223693 | − | 0.974660i | \(-0.428189\pi\) | ||||
0.223693 | + | 0.974660i | \(0.428189\pi\) | |||||||
\(788\) | 1.63966i | 0.0584106i | ||||||||
\(789\) | −37.0968 | − | 1.58272i | −1.32068 | − | 0.0563465i | ||||
\(790\) | 25.4415i | 0.905170i | ||||||||
\(791\) | 31.5725 | 1.12259 | ||||||||
\(792\) | 13.6493 | + | 1.16681i | 0.485007 | + | 0.0414609i | ||||
\(793\) | 0.326653 | 0.0115998 | ||||||||
\(794\) | 19.2875i | 0.684488i | ||||||||
\(795\) | 1.39920 | − | 32.7951i | 0.0496244 | − | 1.16312i | ||||
\(796\) | −20.5203 | −0.727322 | ||||||||
\(797\) | −3.93475 | −0.139376 | −0.0696880 | − | 0.997569i | \(-0.522200\pi\) | ||||
−0.0696880 | + | 0.997569i | \(0.522200\pi\) | |||||||
\(798\) | 0.315516 | − | 7.39522i | 0.0111691 | − | 0.261788i | ||||
\(799\) | 1.70543i | 0.0603339i | ||||||||
\(800\) | 0.313957 | 0.0111000 | ||||||||
\(801\) | −12.8091 | − | 1.09499i | −0.452589 | − | 0.0386896i | ||||
\(802\) | −4.84743 | −0.171169 | ||||||||
\(803\) | 61.5104i | 2.17066i | ||||||||
\(804\) | −5.76871 | − | 0.246121i | −0.203447 | − | 0.00868001i | ||||
\(805\) | 63.4168i | 2.23515i | ||||||||
\(806\) | −4.42437 | −0.155842 | ||||||||
\(807\) | −0.753084 | + | 17.6512i | −0.0265098 | + | 0.621352i | ||||
\(808\) | −8.85165 | −0.311400 | ||||||||
\(809\) | 10.6503 | 0.374444 | 0.187222 | − | 0.982318i | \(-0.440052\pi\) | ||||
0.187222 | + | 0.982318i | \(0.440052\pi\) | |||||||
\(810\) | −3.52136 | + | 20.4458i | −0.123728 | + | 0.718392i | ||||
\(811\) | − | 36.7153i | − | 1.28925i | −0.764499 | − | 0.644625i | \(-0.777014\pi\) | ||
0.764499 | − | 0.644625i | \(-0.222986\pi\) | |||||||
\(812\) | − | 24.6623i | − | 0.865476i | ||||||
\(813\) | −1.37817 | + | 32.3023i | −0.0483346 | + | 1.13289i | ||||
\(814\) | − | 12.9393i | − | 0.453522i | ||||||
\(815\) | 4.78006i | 0.167438i | ||||||||
\(816\) | 4.37689 | + | 0.186739i | 0.153222 | + | 0.00653717i | ||||
\(817\) | 15.1758i | 0.530933i | ||||||||
\(818\) | − | 36.9306i | − | 1.29125i | ||||||
\(819\) | −2.03110 | + | 23.7596i | −0.0709722 | + | 0.830229i | ||||
\(820\) | 13.3177 | 0.465073 | ||||||||
\(821\) | −40.0031 | −1.39612 | −0.698058 | − | 0.716041i | \(-0.745952\pi\) | ||||
−0.698058 | + | 0.716041i | \(0.745952\pi\) | |||||||
\(822\) | 23.7442 | + | 1.01304i | 0.828176 | + | 0.0353339i | ||||
\(823\) | 47.8113i | 1.66660i | 0.552824 | + | 0.833298i | \(0.313550\pi\) | ||||
−0.552824 | + | 0.833298i | \(0.686450\pi\) | |||||||
\(824\) | 13.6040i | 0.473918i | ||||||||
\(825\) | −0.105846 | + | 2.48088i | −0.00368509 | + | 0.0863731i | ||||
\(826\) | −24.4470 | − | 5.14357i | −0.850618 | − | 0.178968i | ||||
\(827\) | 43.6206i | 1.51684i | 0.651768 | + | 0.758418i | \(0.274027\pi\) | ||||
−0.651768 | + | 0.758418i | \(0.725973\pi\) | |||||||
\(828\) | 25.2831 | + | 2.16133i | 0.878650 | + | 0.0751115i | ||||
\(829\) | 18.2431 | 0.633610 | 0.316805 | − | 0.948491i | \(-0.397390\pi\) | ||||
0.316805 | + | 0.948491i | \(0.397390\pi\) | |||||||
\(830\) | − | 21.9592i | − | 0.762214i | ||||||
\(831\) | −1.23701 | + | 28.9938i | −0.0429115 | + | 1.00578i | ||||
\(832\) | − | 2.44397i | − | 0.0847292i | ||||||
\(833\) | 9.05015i | 0.313569i | ||||||||
\(834\) | 1.51727 | − | 35.5626i | 0.0525387 | − | 1.23143i | ||||
\(835\) | −40.8471 | −1.41357 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | −9.32986 | − | 1.20000i | −0.322487 | − | 0.0414780i | ||||
\(838\) | 24.1961 | 0.835839 | ||||||||
\(839\) | −33.0019 | −1.13935 | −0.569676 | − | 0.821869i | \(-0.692931\pi\) | ||||
−0.569676 | + | 0.821869i | \(0.692931\pi\) | |||||||
\(840\) | 12.9742 | + | 0.553540i | 0.447651 | + | 0.0190989i | ||||
\(841\) | −28.4985 | −0.982708 | ||||||||
\(842\) | 23.5993i | 0.813287i | ||||||||
\(843\) | 34.7837 | + | 1.48404i | 1.19802 | + | 0.0511131i | ||||
\(844\) | 17.9919i | 0.619308i | ||||||||
\(845\) | − | 16.1987i | − | 0.557253i | ||||||
\(846\) | 2.01547 | + | 0.172292i | 0.0692932 | + | 0.00592354i | ||||
\(847\) | 32.0415 | 1.10096 | ||||||||
\(848\) | 8.22118i | 0.282317i | ||||||||
\(849\) | 27.9823 | + | 1.19386i | 0.960350 | + | 0.0409731i | ||||
\(850\) | 0.794089i | 0.0272370i | ||||||||
\(851\) | − | 23.9680i | − | 0.821611i | ||||||
\(852\) | 11.0014 | + | 0.469371i | 0.376901 | + | 0.0160804i | ||||
\(853\) | 29.6827 | 1.01631 | 0.508157 | − | 0.861264i | \(-0.330327\pi\) | ||||
0.508157 | + | 0.861264i | \(0.330327\pi\) | |||||||
\(854\) | − | 0.434706i | − | 0.0148753i | ||||||
\(855\) | 0.773964 | − | 9.05379i | 0.0264690 | − | 0.309633i | ||||
\(856\) | − | 11.2988i | − | 0.386185i | ||||||
\(857\) | −46.4927 | −1.58816 | −0.794080 | − | 0.607814i | \(-0.792047\pi\) | ||||
−0.794080 | + | 0.607814i | \(0.792047\pi\) | |||||||
\(858\) | 19.3122 | + | 0.823949i | 0.659306 | + | 0.0281292i | ||||
\(859\) | − | 9.94325i | − | 0.339259i | −0.985508 | − | 0.169630i | \(-0.945743\pi\) | ||
0.985508 | − | 0.169630i | \(-0.0542572\pi\) | |||||||
\(860\) | −26.6243 | −0.907882 | ||||||||
\(861\) | 32.5154 | + | 1.38726i | 1.10812 | + | 0.0472777i | ||||
\(862\) | −30.4771 | −1.03806 | ||||||||
\(863\) | −19.8257 | −0.674874 | −0.337437 | − | 0.941348i | \(-0.609560\pi\) | ||||
−0.337437 | + | 0.941348i | \(0.609560\pi\) | |||||||
\(864\) | 0.662864 | − | 5.15370i | 0.0225511 | − | 0.175332i | ||||
\(865\) | − | 2.46074i | − | 0.0836677i | ||||||
\(866\) | 37.7340 | 1.28225 | ||||||||
\(867\) | 0.782799 | − | 18.3477i | 0.0265853 | − | 0.623119i | ||||
\(868\) | 5.88790i | 0.199848i | ||||||||
\(869\) | 50.3970 | 1.70960 | ||||||||
\(870\) | 1.29054 | − | 30.2484i | 0.0437535 | − | 1.02552i | ||||
\(871\) | −8.14719 | −0.276057 | ||||||||
\(872\) | − | 19.2424i | − | 0.651631i | ||||||
\(873\) | 2.19301 | − | 25.6536i | 0.0742220 | − | 0.868244i | ||||
\(874\) | −11.1140 | −0.375938 | ||||||||
\(875\) | − | 35.1334i | − | 1.18772i | ||||||
\(876\) | 23.3101 | + | 0.994520i | 0.787575 | + | 0.0336017i | ||||
\(877\) | 9.44847 | 0.319052 | 0.159526 | − | 0.987194i | \(-0.449003\pi\) | ||||
0.159526 | + | 0.987194i | \(0.449003\pi\) | |||||||
\(878\) | 6.37650 | 0.215197 | ||||||||
\(879\) | −23.7235 | − | 1.01216i | −0.800174 | − | 0.0341392i | ||||
\(880\) | − | 10.5264i | − | 0.354844i | ||||||
\(881\) | −22.2975 | −0.751223 | −0.375612 | − | 0.926777i | \(-0.622567\pi\) | ||||
−0.375612 | + | 0.926777i | \(0.622567\pi\) | |||||||
\(882\) | 10.6954 | + | 0.914297i | 0.360132 | + | 0.0307860i | ||||
\(883\) | −46.4123 | −1.56190 | −0.780949 | − | 0.624595i | \(-0.785264\pi\) | ||||
−0.780949 | + | 0.624595i | \(0.785264\pi\) | |||||||
\(884\) | 6.18151 | 0.207907 | ||||||||
\(885\) | −29.7152 | − | 7.58791i | −0.998866 | − | 0.255065i | ||||
\(886\) | 21.9885 | 0.738718 | ||||||||
\(887\) | 1.77193 | 0.0594956 | 0.0297478 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297478 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(888\) | −4.90350 | − | 0.209207i | −0.164551 | − | 0.00702051i | ||||
\(889\) | −10.2151 | −0.342605 | ||||||||
\(890\) | 9.87846i | 0.331127i | ||||||||
\(891\) | 40.5009 | + | 6.97543i | 1.35683 | + | 0.233686i | ||||
\(892\) | 12.8745 | 0.431069 | ||||||||
\(893\) | −0.885965 | −0.0296477 | ||||||||
\(894\) | −1.26238 | + | 29.5884i | −0.0422204 | + | 0.989584i | ||||
\(895\) | − | 29.1807i | − | 0.975404i | ||||||
\(896\) | −3.25240 | −0.108655 | ||||||||
\(897\) | 35.7727 | + | 1.52623i | 1.19441 | + | 0.0509594i | ||||
\(898\) | 23.7841i | 0.793687i | ||||||||
\(899\) | 13.7273 | 0.457830 | ||||||||
\(900\) | 0.938447 | + | 0.0802233i | 0.0312816 | + | 0.00267411i | ||||
\(901\) | −20.7938 | −0.692742 | ||||||||
\(902\) | − | 26.3809i | − | 0.878386i | ||||||
\(903\) | −65.0040 | − | 2.77338i | −2.16320 | − | 0.0922923i | ||||
\(904\) | −9.70743 | −0.322864 | ||||||||
\(905\) | − | 28.1318i | − | 0.935133i | ||||||
\(906\) | 24.1659 | + | 1.03103i | 0.802858 | + | 0.0342537i | ||||
\(907\) | 9.37900 | 0.311425 | 0.155712 | − | 0.987802i | \(-0.450233\pi\) | ||||
0.155712 | + | 0.987802i | \(0.450233\pi\) | |||||||
\(908\) | −6.85578 | −0.227517 | ||||||||
\(909\) | −26.4584 | − | 2.26180i | −0.877571 | − | 0.0750193i | ||||
\(910\) | 18.3235 | 0.607418 | ||||||||
\(911\) | − | 52.5106i | − | 1.73975i | −0.493269 | − | 0.869877i | \(-0.664198\pi\) | ||
0.493269 | − | 0.869877i | \(-0.335802\pi\) | |||||||
\(912\) | −0.0970099 | + | 2.27377i | −0.00321232 | + | 0.0752921i | ||||
\(913\) | −43.4988 | −1.43960 | ||||||||
\(914\) | − | 8.86945i | − | 0.293375i | ||||||
\(915\) | 0.0227476 | − | 0.533170i | 0.000752012 | − | 0.0176261i | ||||
\(916\) | 19.9984i | 0.660766i | ||||||||
\(917\) | 35.6449 | 1.17710 | ||||||||
\(918\) | 13.0352 | + | 1.67658i | 0.430226 | + | 0.0553353i | ||||
\(919\) | − | 43.5065i | − | 1.43515i | −0.696483 | − | 0.717573i | \(-0.745253\pi\) | ||
0.696483 | − | 0.717573i | \(-0.254747\pi\) | |||||||
\(920\) | − | 19.4984i | − | 0.642844i | ||||||
\(921\) | −0.351133 | + | 8.23005i | −0.0115702 | + | 0.271189i | ||||
\(922\) | 17.7652i | 0.585066i | ||||||||
\(923\) | 15.5373 | 0.511417 | ||||||||
\(924\) | 1.09650 | − | 25.7004i | 0.0360723 | − | 0.845482i | ||||
\(925\) | − | 0.889631i | − | 0.0292509i | ||||||
\(926\) | 27.7798i | 0.912901i | ||||||||
\(927\) | −3.47614 | + | 40.6637i | −0.114171 | + | 1.33557i | ||||
\(928\) | 7.58278i | 0.248917i | ||||||||
\(929\) | 16.6357 | 0.545801 | 0.272900 | − | 0.962042i | \(-0.412017\pi\) | ||||
0.272900 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(930\) | −0.308106 | + | 7.22156i | −0.0101032 | + | 0.236804i | ||||
\(931\) | −4.70151 | −0.154086 | ||||||||
\(932\) | 3.71058 | 0.121544 | ||||||||
\(933\) | 10.1788 | + | 0.434278i | 0.333240 | + | 0.0142176i | ||||
\(934\) | −8.59729 | −0.281312 | ||||||||
\(935\) | 26.6243 | 0.870709 | ||||||||
\(936\) | 0.624491 | − | 7.30525i | 0.0204121 | − | 0.238780i | ||||
\(937\) | 41.3803i | 1.35184i | 0.736977 | + | 0.675918i | \(0.236253\pi\) | ||||
−0.736977 | + | 0.675918i | \(0.763747\pi\) | |||||||
\(938\) | 10.8422i | 0.354010i | ||||||||
\(939\) | −2.22716 | − | 0.0950212i | −0.0726806 | − | 0.00310090i | ||||
\(940\) | − | 1.55433i | − | 0.0506968i | ||||||
\(941\) | 6.61621 | 0.215682 | 0.107841 | − | 0.994168i | \(-0.465606\pi\) | ||||
0.107841 | + | 0.994168i | \(0.465606\pi\) | |||||||
\(942\) | 21.3982 | + | 0.912948i | 0.697190 | + | 0.0297454i | ||||
\(943\) | − | 48.8663i | − | 1.59131i | ||||||
\(944\) | 7.51658 | + | 1.58147i | 0.244644 | + | 0.0514724i | ||||
\(945\) | 38.6396 | + | 4.96979i | 1.25695 | + | 0.161667i | ||||
\(946\) | 52.7400i | 1.71472i | ||||||||
\(947\) | − | 29.6511i | − | 0.963531i | −0.876300 | − | 0.481765i | \(-0.839996\pi\) | ||
0.876300 | − | 0.481765i | \(-0.160004\pi\) | |||||||
\(948\) | 0.814835 | − | 19.0985i | 0.0264646 | − | 0.620292i | ||||
\(949\) | 32.9210 | 1.06866 | ||||||||
\(950\) | −0.412525 | −0.0133841 | ||||||||
\(951\) | 45.6776 | + | 1.94882i | 1.48120 | + | 0.0631949i | ||||
\(952\) | − | 8.22629i | − | 0.266616i | ||||||
\(953\) | 8.40629i | 0.272307i | 0.990688 | + | 0.136153i | \(0.0434740\pi\) | ||||
−0.990688 | + | 0.136153i | \(0.956526\pi\) | |||||||
\(954\) | −2.10071 | + | 24.5739i | −0.0680129 | + | 0.795610i | ||||
\(955\) | 40.3217i | 1.30478i | ||||||||
\(956\) | 27.3300i | 0.883914i | ||||||||
\(957\) | −59.9190 | − | 2.55643i | −1.93690 | − | 0.0826376i | ||||
\(958\) | 33.5116i | 1.08271i | ||||||||
\(959\) | − | 44.6269i | − | 1.44108i | ||||||
\(960\) | −3.98910 | − | 0.170194i | −0.128748 | − | 0.00549299i | ||||
\(961\) | 27.7227 | 0.894282 | ||||||||
\(962\) | −6.92525 | −0.223279 | ||||||||
\(963\) | 2.88711 | − | 33.7732i | 0.0930357 | − | 1.08833i | ||||
\(964\) | −20.6469 | −0.664991 | ||||||||
\(965\) | − | 9.05178i | − | 0.291387i | ||||||
\(966\) | 2.03110 | − | 47.6059i | 0.0653494 | − | 1.53170i | ||||
\(967\) | − | 1.73649i | − | 0.0558419i | −0.999610 | − | 0.0279210i | \(-0.991111\pi\) | ||
0.999610 | − | 0.0279210i | \(-0.00888867\pi\) | |||||||
\(968\) | −9.85165 | −0.316644 | ||||||||
\(969\) | −5.75104 | − | 0.245367i | −0.184750 | − | 0.00788232i | ||||
\(970\) | −19.7842 | −0.635232 | ||||||||
\(971\) | − | 10.7342i | − | 0.344477i | −0.985055 | − | 0.172239i | \(-0.944900\pi\) | ||
0.985055 | − | 0.172239i | \(-0.0551000\pi\) | |||||||
\(972\) | 3.29826 | − | 15.2355i | 0.105792 | − | 0.488680i | ||||
\(973\) | −66.8393 | −2.14277 | ||||||||
\(974\) | −15.2524 | −0.488719 | ||||||||
\(975\) | 1.32779 | + | 0.0566500i | 0.0425234 | + | 0.00181425i | ||||
\(976\) | 0.133657i | 0.00427825i | ||||||||
\(977\) | −54.0683 | −1.72980 | −0.864899 | − | 0.501946i | \(-0.832618\pi\) | ||||
−0.864899 | + | 0.501946i | \(0.832618\pi\) | |||||||
\(978\) | 0.153094 | − | 3.58831i | 0.00489542 | − | 0.114742i | ||||
\(979\) | 19.5682 | 0.625402 | ||||||||
\(980\) | − | 8.24832i | − | 0.263483i | ||||||
\(981\) | 4.91690 | − | 57.5176i | 0.156984 | − | 1.83639i | ||||
\(982\) | 11.8006i | 0.376571i | ||||||||
\(983\) | 10.8443 | 0.345879 | 0.172939 | − | 0.984932i | \(-0.444674\pi\) | ||||
0.172939 | + | 0.984932i | \(0.444674\pi\) | |||||||
\(984\) | −9.99734 | − | 0.426534i | −0.318704 | − | 0.0135974i | ||||
\(985\) | 3.77976 | 0.120433 | ||||||||
\(986\) | −19.1791 | −0.610786 | ||||||||
\(987\) | 0.161911 | − | 3.79495i | 0.00515367 | − | 0.120794i | ||||
\(988\) | 3.21126i | 0.102164i | ||||||||
\(989\) | 97.6923i | 3.10643i | ||||||||
\(990\) | 2.68974 | − | 31.4644i | 0.0854855 | − | 1.00000i | ||||
\(991\) | − | 46.3054i | − | 1.47094i | −0.677557 | − | 0.735470i | \(-0.736961\pi\) | ||
0.677557 | − | 0.735470i | \(-0.263039\pi\) | |||||||
\(992\) | − | 1.81032i | − | 0.0574778i | ||||||
\(993\) | 1.16025 | − | 27.1946i | 0.0368194 | − | 0.862993i | ||||
\(994\) | − | 20.6769i | − | 0.655832i | ||||||
\(995\) | 47.3034i | 1.49962i | ||||||||
\(996\) | −0.703303 | + | 16.4844i | −0.0222850 | + | 0.522328i | ||||
\(997\) | −30.0886 | −0.952916 | −0.476458 | − | 0.879197i | \(-0.658080\pi\) | ||||
−0.476458 | + | 0.879197i | \(0.658080\pi\) | |||||||
\(998\) | 13.2132 | 0.418258 | ||||||||
\(999\) | −14.6036 | − | 1.87830i | −0.462037 | − | 0.0594267i |
(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 | 354.2.c.a.353.5 | ✓ | 10 | |
3.2 | odd | 2 | 354.2.c.b.353.6 | yes | 10 | ||
59.58 | odd | 2 | 354.2.c.b.353.5 | yes | 10 | ||
177.176 | even | 2 | inner | 354.2.c.a.353.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.2.c.a.353.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
354.2.c.a.353.6 | yes | 10 | 177.176 | even | 2 | inner | |
354.2.c.b.353.5 | yes | 10 | 59.58 | odd | 2 | ||
354.2.c.b.353.6 | yes | 10 | 3.2 | odd | 2 |