Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(117,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.117");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 117.2 | ||
Character | \(\chi\) | \(=\) | 392.117 |
Dual form | 392.3.j.e.325.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87135 | − | 0.705725i | −0.935675 | − | 0.352863i | ||||
\(3\) | 0.126628 | + | 0.219326i | 0.0422093 | + | 0.0731087i | 0.886358 | − | 0.463000i | \(-0.153227\pi\) |
−0.844149 | + | 0.536109i | \(0.819894\pi\) | |||||||
\(4\) | 3.00390 | + | 2.64132i | 0.750976 | + | 0.660330i | ||||
\(5\) | −1.78589 | + | 3.09325i | −0.357178 | + | 0.618650i | −0.987488 | − | 0.157693i | \(-0.949594\pi\) |
0.630310 | + | 0.776343i | \(0.282928\pi\) | |||||||
\(6\) | −0.0821813 | − | 0.499801i | −0.0136969 | − | 0.0833001i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.75731 | − | 7.06276i | −0.469664 | − | 0.882845i | ||||
\(9\) | 4.46793 | − | 7.73868i | 0.496437 | − | 0.859854i | ||||
\(10\) | 5.52501 | − | 4.52821i | 0.552501 | − | 0.452821i | ||||
\(11\) | −6.82675 | + | 3.94142i | −0.620613 | + | 0.358311i | −0.777108 | − | 0.629368i | \(-0.783314\pi\) |
0.156494 | + | 0.987679i | \(0.449981\pi\) | |||||||
\(12\) | −0.198932 | + | 0.993300i | −0.0165777 | + | 0.0827750i | ||||
\(13\) | −18.1529 | −1.39638 | −0.698189 | − | 0.715914i | \(-0.746010\pi\) | ||||
−0.698189 | + | 0.715914i | \(0.746010\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.904575 | −0.0603050 | ||||||||
\(16\) | 2.04687 | + | 15.8685i | 0.127929 | + | 0.991783i | ||||
\(17\) | 8.26180 | − | 4.76995i | 0.485988 | − | 0.280585i | −0.236920 | − | 0.971529i | \(-0.576138\pi\) |
0.722909 | + | 0.690944i | \(0.242805\pi\) | |||||||
\(18\) | −13.8224 | + | 11.3287i | −0.767914 | + | 0.629370i | ||||
\(19\) | 12.4094 | − | 21.4938i | 0.653129 | − | 1.13125i | −0.329231 | − | 0.944250i | \(-0.606789\pi\) |
0.982359 | − | 0.187003i | \(-0.0598773\pi\) | |||||||
\(20\) | −13.5349 | + | 4.57472i | −0.676745 | + | 0.228736i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.5568 | − | 2.55798i | 0.707127 | − | 0.116272i | ||||
\(23\) | 2.14949 | − | 3.72303i | 0.0934563 | − | 0.161871i | −0.815507 | − | 0.578747i | \(-0.803542\pi\) |
0.908963 | + | 0.416876i | \(0.136875\pi\) | |||||||
\(24\) | 1.07327 | − | 1.71842i | 0.0447195 | − | 0.0716008i | ||||
\(25\) | 6.12120 | + | 10.6022i | 0.244848 | + | 0.424089i | ||||
\(26\) | 33.9704 | + | 12.8110i | 1.30656 | + | 0.492729i | ||||
\(27\) | 4.54237 | 0.168236 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 28.3630i | − | 0.978035i | −0.872274 | − | 0.489017i | \(-0.837356\pi\) | ||
0.872274 | − | 0.489017i | \(-0.162644\pi\) | |||||||
\(30\) | 1.69278 | + | 0.638381i | 0.0564259 | + | 0.0212794i | ||||
\(31\) | 28.2372 | − | 16.3027i | 0.910876 | − | 0.525895i | 0.0301634 | − | 0.999545i | \(-0.490397\pi\) |
0.880713 | + | 0.473650i | \(0.157064\pi\) | |||||||
\(32\) | 7.36842 | − | 31.1401i | 0.230263 | − | 0.973128i | ||||
\(33\) | −1.72891 | − | 0.998189i | −0.0523914 | − | 0.0302482i | ||||
\(34\) | −18.8270 | + | 3.09569i | −0.553735 | + | 0.0910497i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 33.8616 | − | 11.4450i | 0.940599 | − | 0.317917i | ||||
\(37\) | 25.9006 | + | 14.9537i | 0.700017 | + | 0.404155i | 0.807354 | − | 0.590068i | \(-0.200899\pi\) |
−0.107337 | + | 0.994223i | \(0.534232\pi\) | |||||||
\(38\) | −38.3911 | + | 31.4648i | −1.01029 | + | 0.828020i | ||||
\(39\) | −2.29867 | − | 3.98141i | −0.0589402 | − | 0.102087i | ||||
\(40\) | 28.5570 | + | 0.991016i | 0.713926 | + | 0.0247754i | ||||
\(41\) | − | 45.2606i | − | 1.10392i | −0.833872 | − | 0.551958i | \(-0.813881\pi\) | ||
0.833872 | − | 0.551958i | \(-0.186119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 24.9109i | − | 0.579323i | −0.957129 | − | 0.289661i | \(-0.906457\pi\) | ||
0.957129 | − | 0.289661i | \(-0.0935427\pi\) | |||||||
\(44\) | −30.9174 | − | 6.19196i | −0.702669 | − | 0.140726i | ||||
\(45\) | 15.9585 | + | 27.6409i | 0.354632 | + | 0.614242i | ||||
\(46\) | −6.64990 | + | 5.45015i | −0.144563 | + | 0.118481i | ||||
\(47\) | −44.0432 | − | 25.4284i | −0.937090 | − | 0.541029i | −0.0480430 | − | 0.998845i | \(-0.515298\pi\) |
−0.889047 | + | 0.457816i | \(0.848632\pi\) | |||||||
\(48\) | −3.22119 | + | 2.45833i | −0.0671082 | + | 0.0512153i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.97264 | − | 24.1604i | −0.0794529 | − | 0.483207i | ||||
\(51\) | 2.09235 | + | 1.20802i | 0.0410265 | + | 0.0236867i | ||||
\(52\) | −54.5296 | − | 47.9476i | −1.04865 | − | 0.922069i | ||||
\(53\) | −54.3930 | + | 31.4038i | −1.02628 | + | 0.592525i | −0.915918 | − | 0.401366i | \(-0.868535\pi\) |
−0.110365 | + | 0.993891i | \(0.535202\pi\) | |||||||
\(54\) | −8.50036 | − | 3.20566i | −0.157414 | − | 0.0593641i | ||||
\(55\) | − | 28.1558i | − | 0.511924i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.28554 | 0.110273 | ||||||||
\(58\) | −20.0165 | + | 53.0771i | −0.345112 | + | 0.915123i | ||||
\(59\) | −37.0048 | − | 64.0942i | −0.627200 | − | 1.08634i | −0.988111 | − | 0.153741i | \(-0.950868\pi\) |
0.360912 | − | 0.932600i | \(-0.382466\pi\) | |||||||
\(60\) | −2.71725 | − | 2.38927i | −0.0452876 | − | 0.0398212i | ||||
\(61\) | 25.2994 | − | 43.8198i | 0.414743 | − | 0.718357i | −0.580658 | − | 0.814148i | \(-0.697205\pi\) |
0.995401 | + | 0.0957908i | \(0.0305380\pi\) | |||||||
\(62\) | −64.3469 | + | 10.5804i | −1.03785 | + | 0.170652i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −35.7653 | + | 53.0740i | −0.558832 | + | 0.829281i | ||||
\(65\) | 32.4191 | − | 56.1515i | 0.498755 | − | 0.863869i | ||||
\(66\) | 2.53096 | + | 3.08810i | 0.0383478 | + | 0.0467894i | ||||
\(67\) | 108.673 | − | 62.7422i | 1.62198 | − | 0.936451i | 0.635592 | − | 0.772025i | \(-0.280756\pi\) |
0.986389 | − | 0.164426i | \(-0.0525772\pi\) | |||||||
\(68\) | 37.4166 | + | 7.49357i | 0.550244 | + | 0.110200i | ||||
\(69\) | 1.08875 | 0.0157789 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.33822 | −0.0751863 | −0.0375931 | − | 0.999293i | \(-0.511969\pi\) | ||||
−0.0375931 | + | 0.999293i | \(0.511969\pi\) | |||||||
\(72\) | −71.4439 | − | 2.47932i | −0.992276 | − | 0.0344350i | ||||
\(73\) | 23.6569 | − | 13.6583i | 0.324067 | − | 0.187100i | −0.329137 | − | 0.944282i | \(-0.606758\pi\) |
0.653204 | + | 0.757182i | \(0.273424\pi\) | |||||||
\(74\) | −37.9159 | − | 46.2624i | −0.512378 | − | 0.625168i | ||||
\(75\) | −1.55023 | + | 2.68508i | −0.0206697 | + | 0.0358010i | ||||
\(76\) | 94.0487 | − | 31.7880i | 1.23748 | − | 0.418263i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.49183 | + | 9.07283i | 0.0191260 | + | 0.116318i | ||||
\(79\) | 51.5380 | − | 89.2664i | 0.652380 | − | 1.12995i | −0.330164 | − | 0.943924i | \(-0.607104\pi\) |
0.982544 | − | 0.186031i | \(-0.0595626\pi\) | |||||||
\(80\) | −52.7408 | − | 22.0080i | −0.659261 | − | 0.275100i | ||||
\(81\) | −39.6362 | − | 68.6519i | −0.489336 | − | 0.847554i | ||||
\(82\) | −31.9415 | + | 84.6984i | −0.389531 | + | 1.03291i | ||||
\(83\) | 51.5695 | 0.621319 | 0.310660 | − | 0.950521i | \(-0.399450\pi\) | ||||
0.310660 | + | 0.950521i | \(0.399450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.0744i | 0.400876i | ||||||||
\(86\) | −17.5802 | + | 46.6170i | −0.204421 | + | 0.542058i | ||||
\(87\) | 6.22075 | − | 3.59155i | 0.0715029 | − | 0.0412822i | ||||
\(88\) | 53.4875 | + | 33.4066i | 0.607813 | + | 0.379620i | ||||
\(89\) | −133.222 | − | 76.9158i | −1.49688 | − | 0.864222i | −0.496883 | − | 0.867818i | \(-0.665522\pi\) |
−0.999994 | + | 0.00359545i | \(0.998856\pi\) | |||||||
\(90\) | −10.3570 | − | 62.9880i | −0.115078 | − | 0.699867i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.2906 | − | 5.50613i | 0.177072 | − | 0.0598493i | ||||
\(93\) | 7.15123 | + | 4.12877i | 0.0768950 | + | 0.0443953i | ||||
\(94\) | 64.4749 | + | 78.6678i | 0.685903 | + | 0.836892i | ||||
\(95\) | 44.3238 | + | 76.7711i | 0.466566 | + | 0.808117i | ||||
\(96\) | 7.76289 | − | 2.32712i | 0.0808634 | − | 0.0242409i | ||||
\(97\) | 47.0436i | 0.484986i | 0.970153 | + | 0.242493i | \(0.0779651\pi\) | ||||
−0.970153 | + | 0.242493i | \(0.922035\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 70.4400i | 0.711516i | ||||||||
\(100\) | −9.61637 | + | 48.0161i | −0.0961637 | + | 0.480161i | ||||
\(101\) | 74.6727 | + | 129.337i | 0.739333 | + | 1.28056i | 0.952796 | + | 0.303612i | \(0.0981926\pi\) |
−0.213462 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(102\) | −3.06299 | − | 3.73725i | −0.0300293 | − | 0.0366397i | ||||
\(103\) | 17.1847 | + | 9.92160i | 0.166842 | + | 0.0963262i | 0.581096 | − | 0.813835i | \(-0.302624\pi\) |
−0.414254 | + | 0.910161i | \(0.635957\pi\) | |||||||
\(104\) | 68.2061 | + | 128.210i | 0.655827 | + | 1.23279i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 123.951 | − | 20.3810i | 1.16935 | − | 0.192274i | ||||
\(107\) | 7.91877 | + | 4.57190i | 0.0740072 | + | 0.0427281i | 0.536547 | − | 0.843870i | \(-0.319728\pi\) |
−0.462540 | + | 0.886599i | \(0.653062\pi\) | |||||||
\(108\) | 13.6448 | + | 11.9978i | 0.126341 | + | 0.111091i | ||||
\(109\) | −103.229 | + | 59.5992i | −0.947053 | + | 0.546781i | −0.892164 | − | 0.451711i | \(-0.850814\pi\) |
−0.0548888 | + | 0.998492i | \(0.517480\pi\) | |||||||
\(110\) | −19.8703 | + | 52.6894i | −0.180639 | + | 0.478994i | ||||
\(111\) | 7.57425i | 0.0682365i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −124.011 | −1.09744 | −0.548720 | − | 0.836006i | \(-0.684885\pi\) | ||||
−0.548720 | + | 0.836006i | \(0.684885\pi\) | |||||||
\(114\) | −11.7624 | − | 4.43586i | −0.103179 | − | 0.0389111i | ||||
\(115\) | 7.67752 | + | 13.2979i | 0.0667611 | + | 0.115634i | ||||
\(116\) | 74.9157 | − | 85.1997i | 0.645825 | − | 0.734480i | ||||
\(117\) | −81.1059 | + | 140.480i | −0.693213 | + | 1.20068i | ||||
\(118\) | 24.0160 | + | 146.058i | 0.203526 | + | 1.23778i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.39877 | + | 6.38880i | 0.0283231 | + | 0.0532400i | ||||
\(121\) | −29.4303 | + | 50.9749i | −0.243226 | + | 0.421280i | ||||
\(122\) | −78.2687 | + | 64.1477i | −0.641546 | + | 0.525801i | ||||
\(123\) | 9.92683 | − | 5.73126i | 0.0807059 | − | 0.0465956i | ||||
\(124\) | 127.882 | + | 25.6115i | 1.03131 | + | 0.206545i | ||||
\(125\) | −133.022 | −1.06417 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −57.6144 | −0.453656 | −0.226828 | − | 0.973935i | \(-0.572836\pi\) | ||||
−0.226828 | + | 0.973935i | \(0.572836\pi\) | |||||||
\(128\) | 104.385 | − | 74.0795i | 0.815508 | − | 0.578746i | ||||
\(129\) | 5.46361 | − | 3.15441i | 0.0423535 | − | 0.0244528i | ||||
\(130\) | −100.295 | + | 82.2001i | −0.771500 | + | 0.632309i | ||||
\(131\) | 62.1497 | − | 107.646i | 0.474425 | − | 0.821728i | −0.525146 | − | 0.851012i | \(-0.675989\pi\) |
0.999571 | + | 0.0292837i | \(0.00932261\pi\) | |||||||
\(132\) | −2.55696 | − | 7.56508i | −0.0193709 | − | 0.0573112i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −247.644 | + | 40.7196i | −1.84809 | + | 0.303877i | ||||
\(135\) | −8.11216 | + | 14.0507i | −0.0600901 | + | 0.104079i | ||||
\(136\) | −64.7312 | − | 40.4290i | −0.475965 | − | 0.297272i | ||||
\(137\) | 84.7404 | + | 146.775i | 0.618543 | + | 1.07135i | 0.989752 | + | 0.142799i | \(0.0456102\pi\) |
−0.371208 | + | 0.928550i | \(0.621056\pi\) | |||||||
\(138\) | −2.03742 | − | 0.768355i | −0.0147639 | − | 0.00556779i | ||||
\(139\) | 266.497 | 1.91725 | 0.958624 | − | 0.284677i | \(-0.0918862\pi\) | ||||
0.958624 | + | 0.284677i | \(0.0918862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 12.8798i | − | 0.0913459i | ||||||
\(142\) | 9.98969 | + | 3.76732i | 0.0703499 | + | 0.0265304i | ||||
\(143\) | 123.925 | − | 71.5483i | 0.866610 | − | 0.500338i | ||||
\(144\) | 131.947 | + | 55.0594i | 0.916297 | + | 0.382357i | ||||
\(145\) | 87.7339 | + | 50.6532i | 0.605061 | + | 0.349332i | ||||
\(146\) | −53.9093 | + | 8.86421i | −0.369242 | + | 0.0607138i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 38.3054 | + | 113.331i | 0.258820 | + | 0.765753i | ||||
\(149\) | 26.6902 | + | 15.4096i | 0.179129 | + | 0.103420i | 0.586883 | − | 0.809672i | \(-0.300355\pi\) |
−0.407754 | + | 0.913092i | \(0.633688\pi\) | |||||||
\(150\) | 4.79595 | − | 3.93068i | 0.0319730 | − | 0.0262046i | ||||
\(151\) | −11.7448 | − | 20.3425i | −0.0777800 | − | 0.134719i | 0.824512 | − | 0.565845i | \(-0.191450\pi\) |
−0.902292 | + | 0.431126i | \(0.858116\pi\) | |||||||
\(152\) | −198.432 | − | 6.88618i | −1.30547 | − | 0.0453038i | ||||
\(153\) | − | 85.2473i | − | 0.557172i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 116.460i | 0.751352i | ||||||||
\(156\) | 3.61119 | − | 18.0313i | 0.0231487 | − | 0.115585i | ||||
\(157\) | 63.8147 | + | 110.530i | 0.406463 | + | 0.704015i | 0.994491 | − | 0.104826i | \(-0.0334287\pi\) |
−0.588028 | + | 0.808841i | \(0.700095\pi\) | |||||||
\(158\) | −159.443 | + | 130.677i | −1.00913 | + | 0.827070i | ||||
\(159\) | −13.7754 | − | 7.95320i | −0.0866374 | − | 0.0500202i | ||||
\(160\) | 83.1650 | + | 78.4052i | 0.519781 | + | 0.490032i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 25.7238 | + | 156.444i | 0.158789 | + | 0.965704i | ||||
\(163\) | −138.291 | − | 79.8421i | −0.848409 | − | 0.489829i | 0.0117050 | − | 0.999931i | \(-0.496274\pi\) |
−0.860114 | + | 0.510103i | \(0.829607\pi\) | |||||||
\(164\) | 119.548 | − | 135.958i | 0.728949 | − | 0.829015i | ||||
\(165\) | 6.17530 | − | 3.56531i | 0.0374261 | − | 0.0216080i | ||||
\(166\) | −96.5046 | − | 36.3939i | −0.581353 | − | 0.219240i | ||||
\(167\) | 142.792i | 0.855042i | 0.904005 | + | 0.427521i | \(0.140613\pi\) | ||||
−0.904005 | + | 0.427521i | \(0.859387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 160.528 | 0.949869 | ||||||||
\(170\) | 24.0472 | − | 63.7652i | 0.141454 | − | 0.375089i | ||||
\(171\) | −110.889 | − | 192.066i | −0.648474 | − | 1.12319i | ||||
\(172\) | 65.7976 | − | 74.8299i | 0.382544 | − | 0.435057i | ||||
\(173\) | −97.8898 | + | 169.550i | −0.565837 | + | 0.980059i | 0.431134 | + | 0.902288i | \(0.358114\pi\) |
−0.996971 | + | 0.0777710i | \(0.975220\pi\) | |||||||
\(174\) | −14.1758 | + | 2.33091i | −0.0814704 | + | 0.0133960i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −76.5181 | − | 100.263i | −0.434762 | − | 0.569675i | ||||
\(177\) | 9.37168 | − | 16.2322i | 0.0529474 | − | 0.0917075i | ||||
\(178\) | 195.024 | + | 237.955i | 1.09564 | + | 1.33682i | ||||
\(179\) | 129.477 | − | 74.7535i | 0.723334 | − | 0.417617i | −0.0926444 | − | 0.995699i | \(-0.529532\pi\) |
0.815979 | + | 0.578082i | \(0.196199\pi\) | |||||||
\(180\) | −25.0707 | + | 125.182i | −0.139282 | + | 0.695455i | ||||
\(181\) | −91.2994 | −0.504417 | −0.252208 | − | 0.967673i | \(-0.581157\pi\) | ||||
−0.252208 | + | 0.967673i | \(0.581157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8144 | 0.0700242 | ||||||||
\(184\) | −34.3712 | − | 1.19279i | −0.186800 | − | 0.00648253i | ||||
\(185\) | −92.5114 | + | 53.4115i | −0.500062 | + | 0.288711i | ||||
\(186\) | −10.4687 | − | 12.7732i | −0.0562833 | − | 0.0686730i | ||||
\(187\) | −37.6008 | + | 65.1265i | −0.201074 | + | 0.348270i | ||||
\(188\) | −65.1372 | − | 192.717i | −0.346474 | − | 1.02509i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −28.7661 | − | 174.946i | −0.151400 | − | 0.920769i | ||||
\(191\) | −13.9140 | + | 24.0997i | −0.0728480 | + | 0.126176i | −0.900148 | − | 0.435583i | \(-0.856542\pi\) |
0.827300 | + | 0.561760i | \(0.189875\pi\) | |||||||
\(192\) | −16.1694 | − | 1.12361i | −0.0842156 | − | 0.00585212i | ||||
\(193\) | −121.192 | − | 209.911i | −0.627938 | − | 1.08762i | −0.987965 | − | 0.154678i | \(-0.950566\pi\) |
0.360027 | − | 0.932942i | \(-0.382767\pi\) | |||||||
\(194\) | 33.1999 | − | 88.0351i | 0.171133 | − | 0.453789i | ||||
\(195\) | 16.4207 | 0.0842085 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 94.7050i | − | 0.480736i | −0.970682 | − | 0.240368i | \(-0.922732\pi\) | ||
0.970682 | − | 0.240368i | \(-0.0772682\pi\) | |||||||
\(198\) | 49.7113 | − | 131.818i | 0.251067 | − | 0.665747i | ||||
\(199\) | −267.738 | + | 154.579i | −1.34542 | + | 0.776778i | −0.987597 | − | 0.157011i | \(-0.949814\pi\) |
−0.357823 | + | 0.933790i | \(0.616481\pi\) | |||||||
\(200\) | 51.8818 | − | 83.0684i | 0.259409 | − | 0.415342i | ||||
\(201\) | 27.5220 | + | 15.8899i | 0.136926 | + | 0.0790540i | ||||
\(202\) | −48.4624 | − | 294.733i | −0.239913 | − | 1.45907i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.09445 | + | 9.15534i | 0.0151689 | + | 0.0448791i | ||||
\(205\) | 140.002 | + | 80.8304i | 0.682938 | + | 0.394295i | ||||
\(206\) | −25.1567 | − | 30.6945i | −0.122120 | − | 0.149002i | ||||
\(207\) | −19.2076 | − | 33.2685i | −0.0927903 | − | 0.160717i | ||||
\(208\) | −37.1566 | − | 288.060i | −0.178637 | − | 1.38490i | ||||
\(209\) | 195.644i | 0.936094i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 125.864i | − | 0.596514i | −0.954486 | − | 0.298257i | \(-0.903595\pi\) | ||
0.954486 | − | 0.298257i | \(-0.0964052\pi\) | |||||||
\(212\) | −246.339 | − | 49.3352i | −1.16198 | − | 0.232713i | ||||
\(213\) | −0.675969 | − | 1.17081i | −0.00317356 | − | 0.00549677i | ||||
\(214\) | −11.5923 | − | 14.1441i | −0.0541695 | − | 0.0660940i | ||||
\(215\) | 77.0556 | + | 44.4881i | 0.358398 | + | 0.206921i | ||||
\(216\) | −17.0671 | − | 32.0817i | −0.0790142 | − | 0.148526i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 235.238 | − | 38.6797i | 1.07907 | − | 0.177430i | ||||
\(219\) | 5.99125 | + | 3.45905i | 0.0273573 | + | 0.0157947i | ||||
\(220\) | 74.3684 | − | 84.5773i | 0.338038 | − | 0.384442i | ||||
\(221\) | −149.976 | + | 86.5885i | −0.678623 | + | 0.391803i | ||||
\(222\) | 5.34534 | − | 14.1741i | 0.0240781 | − | 0.0638472i | ||||
\(223\) | − | 8.94619i | − | 0.0401174i | −0.999799 | − | 0.0200587i | \(-0.993615\pi\) | ||
0.999799 | − | 0.0200587i | \(-0.00638532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 109.396 | 0.486206 | ||||||||
\(226\) | 232.067 | + | 87.5175i | 1.02685 | + | 0.387246i | ||||
\(227\) | −136.347 | − | 236.160i | −0.600647 | − | 1.04035i | −0.992723 | − | 0.120419i | \(-0.961576\pi\) |
0.392076 | − | 0.919933i | \(-0.371757\pi\) | |||||||
\(228\) | 18.8811 | + | 16.6021i | 0.0828120 | + | 0.0728162i | ||||
\(229\) | 165.611 | − | 286.846i | 0.723191 | − | 1.25260i | −0.236523 | − | 0.971626i | \(-0.576008\pi\) |
0.959714 | − | 0.280978i | \(-0.0906588\pi\) | |||||||
\(230\) | −4.98269 | − | 30.3032i | −0.0216639 | − | 0.131753i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −200.321 | + | 106.569i | −0.863453 | + | 0.459347i | ||||
\(233\) | −79.1185 | + | 137.037i | −0.339564 | + | 0.588143i | −0.984351 | − | 0.176220i | \(-0.943613\pi\) |
0.644786 | + | 0.764363i | \(0.276946\pi\) | |||||||
\(234\) | 250.918 | − | 205.648i | 1.07230 | − | 0.878837i | ||||
\(235\) | 157.313 | − | 90.8245i | 0.669416 | − | 0.386487i | ||||
\(236\) | 58.1343 | − | 290.274i | 0.246332 | − | 1.22997i | ||||
\(237\) | 26.1046 | 0.110146 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 48.9981 | 0.205013 | 0.102507 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102507 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(240\) | −1.85154 | − | 14.3543i | −0.00771477 | − | 0.0598095i | ||||
\(241\) | −170.914 | + | 98.6771i | −0.709186 | + | 0.409449i | −0.810759 | − | 0.585379i | \(-0.800946\pi\) |
0.101574 | + | 0.994828i | \(0.467612\pi\) | |||||||
\(242\) | 91.0487 | − | 74.6221i | 0.376234 | − | 0.308356i | ||||
\(243\) | 30.4787 | − | 52.7907i | 0.125427 | − | 0.217246i | ||||
\(244\) | 191.739 | − | 64.8067i | 0.785815 | − | 0.265601i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −22.6213 | + | 3.71957i | −0.0919564 | + | 0.0151202i | ||||
\(247\) | −225.267 | + | 390.175i | −0.912014 | + | 1.57965i | ||||
\(248\) | −221.238 | − | 138.178i | −0.892089 | − | 0.557170i | ||||
\(249\) | 6.53014 | + | 11.3105i | 0.0262255 | + | 0.0454239i | ||||
\(250\) | 248.930 | + | 93.8767i | 0.995720 | + | 0.375507i | ||||
\(251\) | −315.497 | −1.25696 | −0.628480 | − | 0.777826i | \(-0.716323\pi\) | ||||
−0.628480 | + | 0.777826i | \(0.716323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.8883i | 0.133946i | ||||||||
\(254\) | 107.817 | + | 40.6599i | 0.424475 | + | 0.160078i | ||||
\(255\) | −7.47341 | + | 4.31478i | −0.0293075 | + | 0.0169207i | ||||
\(256\) | −247.621 | + | 64.9616i | −0.967268 | + | 0.253756i | ||||
\(257\) | 329.533 | + | 190.256i | 1.28223 | + | 0.740296i | 0.977256 | − | 0.212065i | \(-0.0680188\pi\) |
0.304974 | + | 0.952361i | \(0.401352\pi\) | |||||||
\(258\) | −12.4505 | + | 2.04721i | −0.0482576 | + | 0.00793492i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 245.698 | − | 83.0445i | 0.944991 | − | 0.319402i | ||||
\(261\) | −219.492 | − | 126.724i | −0.840967 | − | 0.485532i | ||||
\(262\) | −192.273 | + | 157.584i | −0.733865 | + | 0.601464i | ||||
\(263\) | −98.1636 | − | 170.024i | −0.373246 | − | 0.646480i | 0.616817 | − | 0.787106i | \(-0.288422\pi\) |
−0.990063 | + | 0.140626i | \(0.955088\pi\) | |||||||
\(264\) | −0.553910 | + | 15.9614i | −0.00209814 | + | 0.0604599i | ||||
\(265\) | − | 224.335i | − | 0.846547i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 38.9588i | − | 0.145913i | ||||||
\(268\) | 492.165 | + | 98.5678i | 1.83644 | + | 0.367790i | ||||
\(269\) | −51.1557 | − | 88.6043i | −0.190170 | − | 0.329384i | 0.755137 | − | 0.655568i | \(-0.227571\pi\) |
−0.945306 | + | 0.326184i | \(0.894237\pi\) | |||||||
\(270\) | 25.0966 | − | 20.5688i | 0.0929504 | − | 0.0761807i | ||||
\(271\) | 221.981 | + | 128.161i | 0.819118 | + | 0.472918i | 0.850112 | − | 0.526602i | \(-0.176534\pi\) |
−0.0309944 | + | 0.999520i | \(0.509867\pi\) | |||||||
\(272\) | 92.6030 | + | 121.339i | 0.340452 | + | 0.446100i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −54.9964 | − | 334.470i | −0.200717 | − | 1.22070i | ||||
\(275\) | −83.5757 | − | 48.2525i | −0.303912 | − | 0.175464i | ||||
\(276\) | 3.27048 | + | 2.87572i | 0.0118496 | + | 0.0104193i | ||||
\(277\) | −170.372 | + | 98.3646i | −0.615063 | + | 0.355107i | −0.774944 | − | 0.632029i | \(-0.782222\pi\) |
0.159881 | + | 0.987136i | \(0.448889\pi\) | |||||||
\(278\) | −498.710 | − | 188.074i | −1.79392 | − | 0.676525i | ||||
\(279\) | − | 291.358i | − | 1.04429i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −70.2923 | −0.250151 | −0.125075 | − | 0.992147i | \(-0.539917\pi\) | ||||
−0.125075 | + | 0.992147i | \(0.539917\pi\) | |||||||
\(282\) | −9.08959 | + | 24.1026i | −0.0322326 | + | 0.0854701i | ||||
\(283\) | 148.495 | + | 257.201i | 0.524718 | + | 0.908838i | 0.999586 | + | 0.0287807i | \(0.00916244\pi\) |
−0.474868 | + | 0.880057i | \(0.657504\pi\) | |||||||
\(284\) | −16.0355 | − | 14.1000i | −0.0564631 | − | 0.0496477i | ||||
\(285\) | −11.2253 | + | 19.4427i | −0.0393869 | + | 0.0682201i | ||||
\(286\) | −282.401 | + | 46.4347i | −0.987416 | + | 0.162359i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −208.062 | − | 196.154i | −0.722437 | − | 0.681089i | ||||
\(289\) | −98.9951 | + | 171.465i | −0.342544 | + | 0.593303i | ||||
\(290\) | −128.434 | − | 156.706i | −0.442874 | − | 0.540365i | ||||
\(291\) | −10.3179 | + | 5.95704i | −0.0354567 | + | 0.0204709i | ||||
\(292\) | 107.139 | + | 21.4571i | 0.366914 | + | 0.0734834i | ||||
\(293\) | −135.561 | −0.462665 | −0.231333 | − | 0.972875i | \(-0.574309\pi\) | ||||
−0.231333 | + | 0.972875i | \(0.574309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 264.346 | 0.896087 | ||||||||
\(296\) | 8.29805 | − | 239.116i | 0.0280339 | − | 0.807824i | ||||
\(297\) | −31.0096 | + | 17.9034i | −0.104409 | + | 0.0602808i | ||||
\(298\) | −39.0718 | − | 47.6727i | −0.131113 | − | 0.159976i | ||||
\(299\) | −39.0196 | + | 67.5839i | −0.130500 | + | 0.226033i | ||||
\(300\) | −11.7489 | + | 3.97106i | −0.0391630 | + | 0.0132369i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.62233 | + | 46.3566i | 0.0252395 | + | 0.153499i | ||||
\(303\) | −18.9113 | + | 32.7553i | −0.0624136 | + | 0.108103i | ||||
\(304\) | 366.475 | + | 152.925i | 1.20551 | + | 0.503042i | ||||
\(305\) | 90.3637 | + | 156.515i | 0.296274 | + | 0.513162i | ||||
\(306\) | −60.1612 | + | 159.527i | −0.196605 | + | 0.521332i | ||||
\(307\) | −76.2052 | −0.248225 | −0.124113 | − | 0.992268i | \(-0.539608\pi\) | ||||
−0.124113 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.02541i | 0.0162635i | ||||||||
\(310\) | 82.1885 | − | 217.937i | 0.265124 | − | 0.703021i | ||||
\(311\) | 171.554 | − | 99.0468i | 0.551621 | − | 0.318479i | −0.198154 | − | 0.980171i | \(-0.563495\pi\) |
0.749776 | + | 0.661692i | \(0.230161\pi\) | |||||||
\(312\) | −19.4829 | + | 31.1943i | −0.0624453 | + | 0.0999817i | ||||
\(313\) | 47.9693 | + | 27.6951i | 0.153257 | + | 0.0884827i | 0.574667 | − | 0.818387i | \(-0.305132\pi\) |
−0.421411 | + | 0.906870i | \(0.638465\pi\) | |||||||
\(314\) | −41.4156 | − | 251.877i | −0.131897 | − | 0.802155i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 390.596 | − | 132.019i | 1.23606 | − | 0.417783i | ||||
\(317\) | −259.080 | − | 149.580i | −0.817289 | − | 0.471862i | 0.0321920 | − | 0.999482i | \(-0.489751\pi\) |
−0.849481 | + | 0.527620i | \(0.823085\pi\) | |||||||
\(318\) | 20.1657 | + | 24.6048i | 0.0634143 | + | 0.0773737i | ||||
\(319\) | 111.791 | + | 193.627i | 0.350441 | + | 0.606981i | ||||
\(320\) | −100.298 | − | 205.415i | −0.313432 | − | 0.641923i | ||||
\(321\) | 2.31572i | 0.00721409i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 236.770i | − | 0.733034i | ||||||
\(324\) | 62.2683 | − | 310.915i | 0.192186 | − | 0.959616i | ||||
\(325\) | −111.117 | − | 192.461i | −0.341900 | − | 0.592188i | ||||
\(326\) | 202.444 | + | 247.008i | 0.620992 | + | 0.757693i | ||||
\(327\) | −26.1433 | − | 15.0938i | −0.0799490 | − | 0.0461586i | ||||
\(328\) | −319.665 | + | 170.058i | −0.974588 | + | 0.518469i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −14.0723 | + | 2.31388i | −0.0426433 | + | 0.00701176i | ||||
\(331\) | 325.087 | + | 187.689i | 0.982135 | + | 0.567036i | 0.902914 | − | 0.429821i | \(-0.141423\pi\) |
0.0792209 | + | 0.996857i | \(0.474757\pi\) | |||||||
\(332\) | 154.910 | + | 136.212i | 0.466596 | + | 0.410276i | ||||
\(333\) | 231.445 | − | 133.625i | 0.695029 | − | 0.401275i | ||||
\(334\) | 100.772 | − | 267.214i | 0.301712 | − | 0.800041i | ||||
\(335\) | 448.203i | 1.33792i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.99043 | −0.0148084 | −0.00740419 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740419 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(338\) | −300.404 | − | 113.289i | −0.888769 | − | 0.335173i | ||||
\(339\) | −15.7032 | − | 27.1988i | −0.0463222 | − | 0.0802324i | ||||
\(340\) | −90.0014 | + | 102.356i | −0.264710 | + | 0.301048i | ||||
\(341\) | −128.512 | + | 222.589i | −0.376868 | + | 0.652755i | ||||
\(342\) | 71.9668 | + | 437.679i | 0.210429 | + | 1.27976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −175.940 | + | 93.5978i | −0.511452 | + | 0.272087i | ||||
\(345\) | −1.94438 | + | 3.36776i | −0.00563588 | + | 0.00976163i | ||||
\(346\) | 302.842 | − | 248.204i | 0.875266 | − | 0.717354i | ||||
\(347\) | −320.772 | + | 185.198i | −0.924414 | + | 0.533711i | −0.885041 | − | 0.465514i | \(-0.845870\pi\) |
−0.0393734 | + | 0.999225i | \(0.512536\pi\) | |||||||
\(348\) | 28.1730 | + | 5.64231i | 0.0809568 | + | 0.0162135i | ||||
\(349\) | −25.6801 | −0.0735821 | −0.0367910 | − | 0.999323i | \(-0.511714\pi\) | ||||
−0.0367910 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −82.4571 | −0.234921 | ||||||||
\(352\) | 72.4340 | + | 241.628i | 0.205779 | + | 0.686442i | ||||
\(353\) | 229.938 | − | 132.755i | 0.651383 | − | 0.376076i | −0.137603 | − | 0.990487i | \(-0.543940\pi\) |
0.788986 | + | 0.614411i | \(0.210606\pi\) | |||||||
\(354\) | −28.9932 | + | 23.7624i | −0.0819017 | + | 0.0671253i | ||||
\(355\) | 9.53348 | − | 16.5125i | 0.0268549 | − | 0.0465140i | ||||
\(356\) | −197.027 | − | 582.929i | −0.553446 | − | 1.63744i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −295.052 | + | 48.5148i | −0.824167 | + | 0.135516i | ||||
\(359\) | 275.228 | − | 476.709i | 0.766651 | − | 1.32788i | −0.172718 | − | 0.984971i | \(-0.555255\pi\) |
0.939369 | − | 0.342908i | \(-0.111412\pi\) | |||||||
\(360\) | 135.260 | − | 216.566i | 0.375722 | − | 0.601573i | ||||
\(361\) | −127.489 | − | 220.817i | −0.353155 | − | 0.611682i | ||||
\(362\) | 170.853 | + | 64.4323i | 0.471970 | + | 0.177990i | ||||
\(363\) | −14.9068 | −0.0410656 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 97.5689i | 0.267312i | ||||||||
\(366\) | −23.9803 | − | 9.04347i | −0.0655199 | − | 0.0247089i | ||||
\(367\) | −180.099 | + | 103.980i | −0.490732 | + | 0.283324i | −0.724878 | − | 0.688877i | \(-0.758104\pi\) |
0.234146 | + | 0.972201i | \(0.424771\pi\) | |||||||
\(368\) | 63.4788 | + | 26.4888i | 0.172497 | + | 0.0719803i | ||||
\(369\) | −350.257 | − | 202.221i | −0.949207 | − | 0.548025i | ||||
\(370\) | 210.815 | − | 34.6639i | 0.569770 | − | 0.0936863i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.5762 | + | 31.2911i | 0.0284307 | + | 0.0841159i | ||||
\(373\) | 393.539 | + | 227.210i | 1.05507 | + | 0.609142i | 0.924063 | − | 0.382240i | \(-0.124847\pi\) |
0.131002 | + | 0.991382i | \(0.458180\pi\) | |||||||
\(374\) | 116.326 | − | 95.3387i | 0.311031 | − | 0.254916i | ||||
\(375\) | −16.8443 | − | 29.1751i | −0.0449180 | − | 0.0778003i | ||||
\(376\) | −14.1106 | + | 406.609i | −0.0375281 | + | 1.08141i | ||||
\(377\) | 514.871i | 1.36570i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 373.244i | 0.984813i | 0.870365 | + | 0.492406i | \(0.163883\pi\) | ||||
−0.870365 | + | 0.492406i | \(0.836117\pi\) | |||||||
\(380\) | −69.6325 | + | 347.686i | −0.183243 | + | 0.914964i | ||||
\(381\) | −7.29559 | − | 12.6363i | −0.0191485 | − | 0.0331662i | ||||
\(382\) | 43.0457 | − | 35.2796i | 0.112685 | − | 0.0923549i | ||||
\(383\) | 270.298 | + | 156.056i | 0.705738 | + | 0.407458i | 0.809481 | − | 0.587146i | \(-0.199749\pi\) |
−0.103743 | + | 0.994604i | \(0.533082\pi\) | |||||||
\(384\) | 29.4656 | + | 13.5138i | 0.0767334 | + | 0.0351922i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 78.6533 | + | 478.345i | 0.203765 | + | 1.23923i | ||||
\(387\) | −192.777 | − | 111.300i | −0.498133 | − | 0.287597i | ||||
\(388\) | −124.257 | + | 141.314i | −0.320251 | + | 0.364213i | ||||
\(389\) | 439.628 | − | 253.819i | 1.13015 | − | 0.652492i | 0.186177 | − | 0.982516i | \(-0.440390\pi\) |
0.943973 | + | 0.330024i | \(0.107057\pi\) | |||||||
\(390\) | −30.7288 | − | 11.5885i | −0.0787918 | − | 0.0297140i | ||||
\(391\) | − | 41.0120i | − | 0.104890i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.4796 | 0.0801007 | ||||||||
\(394\) | −66.8358 | + | 177.226i | −0.169634 | + | 0.449813i | ||||
\(395\) | 184.082 | + | 318.840i | 0.466031 | + | 0.807190i | ||||
\(396\) | −186.055 | + | 211.595i | −0.469835 | + | 0.534331i | ||||
\(397\) | 95.6487 | − | 165.668i | 0.240929 | − | 0.417301i | −0.720050 | − | 0.693922i | \(-0.755881\pi\) |
0.960979 | + | 0.276621i | \(0.0892146\pi\) | |||||||
\(398\) | 610.123 | − | 100.321i | 1.53297 | − | 0.252064i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −155.712 | + | 118.836i | −0.389281 | + | 0.297089i | ||||
\(401\) | 61.2011 | − | 106.004i | 0.152621 | − | 0.264348i | −0.779569 | − | 0.626316i | \(-0.784562\pi\) |
0.932190 | + | 0.361968i | \(0.117895\pi\) | |||||||
\(402\) | −40.2895 | − | 49.1585i | −0.100223 | − | 0.122285i | ||||
\(403\) | −512.587 | + | 295.942i | −1.27193 | + | 0.734347i | ||||
\(404\) | −117.310 | + | 585.750i | −0.290372 | + | 1.44988i | ||||
\(405\) | 283.143 | 0.699120 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −235.756 | −0.579254 | ||||||||
\(408\) | 0.670347 | − | 19.3167i | 0.00164301 | − | 0.0473448i | ||||
\(409\) | 4.57744 | − | 2.64279i | 0.0111918 | − | 0.00646158i | −0.494394 | − | 0.869238i | \(-0.664610\pi\) |
0.505585 | + | 0.862777i | \(0.331277\pi\) | |||||||
\(410\) | −204.949 | − | 250.065i | −0.499877 | − | 0.609915i | ||||
\(411\) | −21.4610 | + | 37.1716i | −0.0522166 | + | 0.0904418i | ||||
\(412\) | 25.4151 | + | 75.1939i | 0.0616872 | + | 0.182509i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.4657 | + | 75.8123i | 0.0301103 | + | 0.183122i | ||||
\(415\) | −92.0975 | + | 159.517i | −0.221922 | + | 0.384379i | ||||
\(416\) | −133.758 | + | 565.283i | −0.321534 | + | 1.35885i | ||||
\(417\) | 33.7460 | + | 58.4498i | 0.0809257 | + | 0.140167i | ||||
\(418\) | 138.071 | − | 366.118i | 0.330313 | − | 0.875880i | ||||
\(419\) | 34.7160 | 0.0828545 | 0.0414272 | − | 0.999142i | \(-0.486810\pi\) | ||||
0.0414272 | + | 0.999142i | \(0.486810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 394.337i | − | 0.936669i | −0.883551 | − | 0.468334i | \(-0.844854\pi\) | ||
0.883551 | − | 0.468334i | \(-0.155146\pi\) | |||||||
\(422\) | −88.8257 | + | 235.536i | −0.210487 | + | 0.558143i | ||||
\(423\) | −393.564 | + | 227.224i | −0.930412 | + | 0.537173i | ||||
\(424\) | 426.169 | + | 266.171i | 1.00512 | + | 0.627762i | ||||
\(425\) | 101.144 | + | 58.3956i | 0.237986 | + | 0.137401i | ||||
\(426\) | 0.438702 | + | 2.66805i | 0.00102982 | + | 0.00626302i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.7114 | + | 34.6495i | 0.0273630 | + | 0.0809569i | ||||
\(429\) | 31.3848 | + | 18.1200i | 0.0731581 | + | 0.0422378i | ||||
\(430\) | −112.802 | − | 137.633i | −0.262329 | − | 0.320076i | ||||
\(431\) | 215.872 | + | 373.901i | 0.500862 | + | 0.867519i | 1.00000 | 0.000995912i | \(0.000317009\pi\) | |
−0.499137 | + | 0.866523i | \(0.666350\pi\) | |||||||
\(432\) | 9.29762 | + | 72.0807i | 0.0215223 | + | 0.166853i | ||||
\(433\) | − | 318.535i | − | 0.735647i | −0.929896 | − | 0.367823i | \(-0.880103\pi\) | ||
0.929896 | − | 0.367823i | \(-0.119897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.6565i | 0.0589803i | ||||||||
\(436\) | −467.510 | − | 93.6300i | −1.07227 | − | 0.214748i | ||||
\(437\) | −53.3481 | − | 92.4016i | −0.122078 | − | 0.211445i | ||||
\(438\) | −8.77058 | − | 10.7013i | −0.0200242 | − | 0.0244321i | ||||
\(439\) | −532.799 | − | 307.612i | −1.21366 | − | 0.700710i | −0.250109 | − | 0.968218i | \(-0.580467\pi\) |
−0.963556 | + | 0.267508i | \(0.913800\pi\) | |||||||
\(440\) | −198.858 | + | 105.790i | −0.451949 | + | 0.240432i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 341.765 | − | 56.1957i | 0.773223 | − | 0.127140i | ||||
\(443\) | −86.4553 | − | 49.9150i | −0.195159 | − | 0.112675i | 0.399237 | − | 0.916848i | \(-0.369275\pi\) |
−0.594395 | + | 0.804173i | \(0.702609\pi\) | |||||||
\(444\) | −20.0060 | + | 22.7523i | −0.0450586 | + | 0.0512440i | ||||
\(445\) | 475.840 | − | 274.726i | 1.06930 | − | 0.617362i | ||||
\(446\) | −6.31355 | + | 16.7415i | −0.0141559 | + | 0.0375369i | ||||
\(447\) | 7.80515i | 0.0174612i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −75.3168 | −0.167743 | −0.0838717 | − | 0.996477i | \(-0.526729\pi\) | ||||
−0.0838717 | + | 0.996477i | \(0.526729\pi\) | |||||||
\(450\) | −204.719 | − | 77.2038i | −0.454931 | − | 0.171564i | ||||
\(451\) | 178.391 | + | 308.983i | 0.395546 | + | 0.685105i | ||||
\(452\) | −372.516 | − | 327.552i | −0.824151 | − | 0.724672i | ||||
\(453\) | 2.97443 | − | 5.15187i | 0.00656608 | − | 0.0113728i | ||||
\(454\) | 88.4889 | + | 538.161i | 0.194909 | + | 1.18538i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −23.6167 | − | 44.3932i | −0.0517910 | − | 0.0973536i | ||||
\(457\) | 104.447 | − | 180.907i | 0.228549 | − | 0.395858i | −0.728830 | − | 0.684695i | \(-0.759935\pi\) |
0.957378 | + | 0.288837i | \(0.0932687\pi\) | |||||||
\(458\) | −512.351 | + | 419.914i | −1.11867 | + | 0.916843i | ||||
\(459\) | 37.5281 | − | 21.6669i | 0.0817606 | − | 0.0472045i | ||||
\(460\) | −12.0614 | + | 60.2243i | −0.0262203 | + | 0.130922i | ||||
\(461\) | 751.461 | 1.63007 | 0.815034 | − | 0.579413i | \(-0.196718\pi\) | ||||
0.815034 | + | 0.579413i | \(0.196718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.56075 | −0.00769060 | −0.00384530 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384530 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(464\) | 450.079 | − | 58.0553i | 0.969998 | − | 0.125119i | ||||
\(465\) | −25.5426 | + | 14.7470i | −0.0549304 | + | 0.0317141i | ||||
\(466\) | 244.769 | − | 200.609i | 0.525256 | − | 0.430491i | ||||
\(467\) | −206.945 | + | 358.440i | −0.443138 | + | 0.767537i | −0.997920 | − | 0.0644583i | \(-0.979468\pi\) |
0.554783 | + | 0.831995i | \(0.312801\pi\) | |||||||
\(468\) | −614.686 | + | 207.760i | −1.31343 | + | 0.443932i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −358.484 | + | 58.9449i | −0.762733 | + | 0.125415i | ||||
\(471\) | −16.1615 | + | 27.9925i | −0.0343131 | + | 0.0594320i | ||||
\(472\) | −313.643 | + | 502.177i | −0.664499 | + | 1.06394i | ||||
\(473\) | 98.1843 | + | 170.060i | 0.207578 | + | 0.359535i | ||||
\(474\) | −48.8509 | − | 18.4227i | −0.103061 | − | 0.0388664i | ||||
\(475\) | 303.843 | 0.639669 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 561.240i | 1.17660i | ||||||||
\(478\) | −91.6927 | − | 34.5792i | −0.191826 | − | 0.0723415i | ||||
\(479\) | 785.798 | − | 453.681i | 1.64050 | − | 0.947142i | 0.659841 | − | 0.751405i | \(-0.270624\pi\) |
0.980657 | − | 0.195737i | \(-0.0627098\pi\) | |||||||
\(480\) | −6.66529 | + | 28.1686i | −0.0138860 | + | 0.0586845i | ||||
\(481\) | −470.172 | − | 271.454i | −0.977488 | − | 0.564353i | ||||
\(482\) | 389.478 | − | 64.0412i | 0.808047 | − | 0.132866i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −223.047 | + | 75.3886i | −0.460840 | + | 0.155762i | ||||
\(485\) | −145.518 | − | 84.0147i | −0.300037 | − | 0.173226i | ||||
\(486\) | −94.2922 | + | 77.2803i | −0.194017 | + | 0.159013i | ||||
\(487\) | −421.452 | − | 729.977i | −0.865405 | − | 1.49893i | −0.866644 | − | 0.498926i | \(-0.833728\pi\) |
0.00123943 | − | 0.999999i | \(-0.499605\pi\) | |||||||
\(488\) | −404.546 | − | 14.0390i | −0.828988 | − | 0.0287684i | ||||
\(489\) | − | 40.4410i | − | 0.0827014i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 144.126i | − | 0.293535i | −0.989171 | − | 0.146768i | \(-0.953113\pi\) | ||
0.989171 | − | 0.146768i | \(-0.0468870\pi\) | |||||||
\(492\) | 44.9573 | + | 9.00378i | 0.0913766 | + | 0.0183004i | ||||
\(493\) | −135.290 | − | 234.329i | −0.274422 | − | 0.475313i | ||||
\(494\) | 696.911 | − | 571.177i | 1.41075 | − | 1.15623i | ||||
\(495\) | −217.889 | − | 125.798i | −0.440179 | − | 0.254138i | ||||
\(496\) | 316.498 | + | 414.713i | 0.638101 | + | 0.836115i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.23805 | − | 25.7745i | −0.00851014 | − | 0.0517560i | ||||
\(499\) | 330.101 | + | 190.584i | 0.661526 | + | 0.381932i | 0.792858 | − | 0.609406i | \(-0.208592\pi\) |
−0.131332 | + | 0.991338i | \(0.541926\pi\) | |||||||
\(500\) | −399.584 | − | 351.352i | −0.799168 | − | 0.702705i | ||||
\(501\) | −31.3180 | + | 18.0815i | −0.0625110 | + | 0.0360908i | ||||
\(502\) | 590.405 | + | 222.654i | 1.17611 | + | 0.443534i | ||||
\(503\) | − | 936.429i | − | 1.86169i | −0.365418 | − | 0.930843i | \(-0.619074\pi\) | ||
0.365418 | − | 0.930843i | \(-0.380926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −533.429 | −1.05629 | ||||||||
\(506\) | 23.9158 | − | 63.4168i | 0.0472645 | − | 0.125330i | ||||
\(507\) | 20.3273 | + | 35.2080i | 0.0400933 | + | 0.0694437i | ||||
\(508\) | −173.068 | − | 152.178i | −0.340685 | − | 0.299563i | ||||
\(509\) | 167.592 | − | 290.278i | 0.329258 | − | 0.570291i | −0.653107 | − | 0.757265i | \(-0.726535\pi\) |
0.982365 | + | 0.186975i | \(0.0598682\pi\) | |||||||
\(510\) | 17.0304 | − | 2.80028i | 0.0333930 | − | 0.00549075i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 509.230 | + | 53.1863i | 0.994590 | + | 0.103880i | ||||
\(513\) | 56.3682 | − | 97.6327i | 0.109880 | − | 0.190317i | ||||
\(514\) | −482.403 | − | 588.596i | −0.938528 | − | 1.14513i | ||||
\(515\) | −61.3800 | + | 35.4378i | −0.119185 | + | 0.0688112i | ||||
\(516\) | 24.7440 | + | 4.95557i | 0.0479534 | + | 0.00960382i | ||||
\(517\) | 400.896 | 0.775427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.5824 | −0.0955345 | ||||||||
\(520\) | −518.393 | − | 17.9898i | −0.996910 | − | 0.0345958i | ||||
\(521\) | 421.675 | − | 243.454i | 0.809357 | − | 0.467283i | −0.0373754 | − | 0.999301i | \(-0.511900\pi\) |
0.846733 | + | 0.532019i | \(0.178566\pi\) | |||||||
\(522\) | 321.315 | + | 392.046i | 0.615545 | + | 0.751046i | ||||
\(523\) | −86.3132 | + | 149.499i | −0.165035 | + | 0.285849i | −0.936668 | − | 0.350220i | \(-0.886107\pi\) |
0.771633 | + | 0.636068i | \(0.219440\pi\) | |||||||
\(524\) | 471.020 | − | 159.202i | 0.898894 | − | 0.303821i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 63.7080 | + | 387.452i | 0.121118 | + | 0.736600i | ||||
\(527\) | 155.527 | − | 269.380i | 0.295117 | − | 0.511157i | ||||
\(528\) | 12.3009 | − | 29.4785i | 0.0232972 | − | 0.0558305i | ||||
\(529\) | 255.259 | + | 442.122i | 0.482532 | + | 0.835770i | ||||
\(530\) | −158.319 | + | 419.809i | −0.298715 | + | 0.792093i | ||||
\(531\) | −661.339 | −1.24546 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 821.611i | 1.54148i | ||||||||
\(534\) | −27.4942 | + | 72.9055i | −0.0514872 | + | 0.136527i | ||||
\(535\) | −28.2841 | + | 16.3298i | −0.0528675 | + | 0.0305230i | ||||
\(536\) | −851.451 | − | 531.788i | −1.58853 | − | 0.992142i | ||||
\(537\) | 32.7908 | + | 18.9318i | 0.0610629 | + | 0.0352547i | ||||
\(538\) | 33.1999 | + | 201.912i | 0.0617099 | + | 0.375300i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −61.4805 | + | 20.7801i | −0.113853 | + | 0.0384816i | ||||
\(541\) | −500.736 | − | 289.100i | −0.925574 | − | 0.534381i | −0.0401652 | − | 0.999193i | \(-0.512788\pi\) |
−0.885409 | + | 0.464812i | \(0.846122\pi\) | |||||||
\(542\) | −324.958 | − | 396.491i | −0.599553 | − | 0.731534i | ||||
\(543\) | −11.5611 | − | 20.0244i | −0.0212911 | − | 0.0368773i | ||||
\(544\) | −87.6604 | − | 292.420i | −0.161140 | − | 0.537537i | ||||
\(545\) | − | 425.750i | − | 0.781193i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 454.579i | 0.831040i | 0.909584 | + | 0.415520i | \(0.136400\pi\) | ||||
−0.909584 | + | 0.415520i | \(0.863600\pi\) | |||||||
\(548\) | −133.127 | + | 664.724i | −0.242932 | + | 1.21300i | ||||
\(549\) | −226.071 | − | 391.567i | −0.411788 | − | 0.713237i | ||||
\(550\) | 122.346 | + | 149.279i | 0.222448 | + | 0.271416i | ||||
\(551\) | −609.629 | − | 351.969i | −1.10640 | − | 0.638783i | ||||
\(552\) | −4.09075 | − | 7.68955i | −0.00741078 | − | 0.0139303i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 388.245 | − | 63.8384i | 0.700803 | − | 0.115232i | ||||
\(555\) | −23.4291 | − | 13.5268i | −0.0422145 | − | 0.0243726i | ||||
\(556\) | 800.532 | + | 703.905i | 1.43981 | + | 1.26602i | ||||
\(557\) | −25.2401 | + | 14.5724i | −0.0453143 | + | 0.0261622i | −0.522486 | − | 0.852648i | \(-0.674995\pi\) |
0.477172 | + | 0.878810i | \(0.341662\pi\) | |||||||
\(558\) | −205.619 | + | 545.233i | −0.368492 | + | 0.977120i | ||||
\(559\) | 452.205i | 0.808953i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.0453 | −0.0339488 | ||||||||
\(562\) | 131.542 | + | 49.6071i | 0.234060 | + | 0.0882688i | ||||
\(563\) | 514.005 | + | 890.283i | 0.912975 | + | 1.58132i | 0.809839 | + | 0.586652i | \(0.199554\pi\) |
0.103136 | + | 0.994667i | \(0.467112\pi\) | |||||||
\(564\) | 34.0196 | − | 38.6896i | 0.0603184 | − | 0.0685986i | ||||
\(565\) | 221.469 | − | 383.596i | 0.391981 | − | 0.678931i | ||||
\(566\) | −96.3730 | − | 586.110i | −0.170270 | − | 1.03553i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0574 | + | 37.7026i | 0.0353122 | + | 0.0663778i | ||||
\(569\) | 409.852 | − | 709.885i | 0.720303 | − | 1.24760i | −0.240576 | − | 0.970630i | \(-0.577336\pi\) |
0.960878 | − | 0.276971i | \(-0.0893305\pi\) | |||||||
\(570\) | 34.7277 | − | 28.4622i | 0.0609257 | − | 0.0499337i | ||||
\(571\) | −140.820 | + | 81.3023i | −0.246620 | + | 0.142386i | −0.618215 | − | 0.786009i | \(-0.712144\pi\) |
0.371596 | + | 0.928395i | \(0.378811\pi\) | |||||||
\(572\) | 561.241 | + | 112.402i | 0.981191 | + | 0.196507i | ||||
\(573\) | −7.04760 | −0.0122995 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 52.6299 | 0.0915303 | ||||||||
\(576\) | 250.926 | + | 513.907i | 0.435635 | + | 0.892199i | ||||
\(577\) | −131.878 | + | 76.1400i | −0.228559 | + | 0.131958i | −0.609907 | − | 0.792473i | \(-0.708793\pi\) |
0.381348 | + | 0.924431i | \(0.375460\pi\) | |||||||
\(578\) | 306.261 | − | 251.007i | 0.529864 | − | 0.434268i | ||||
\(579\) | 30.6926 | − | 53.1611i | 0.0530097 | − | 0.0918154i | ||||
\(580\) | 129.753 | + | 383.890i | 0.223712 | + | 0.661880i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 23.5124 | − | 3.86611i | 0.0403994 | − | 0.00664279i | ||||
\(583\) | 247.551 | − | 428.772i | 0.424617 | − | 0.735457i | ||||
\(584\) | −185.352 | − | 115.764i | −0.317383 | − | 0.198227i | ||||
\(585\) | −289.692 | − | 501.762i | −0.495201 | − | 0.857713i | ||||
\(586\) | 253.682 | + | 95.6688i | 0.432905 | + | 0.163257i | ||||
\(587\) | −894.404 | −1.52369 | −0.761843 | − | 0.647761i | \(-0.775705\pi\) | ||||
−0.761843 | + | 0.647761i | \(0.775705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 809.232i | − | 1.37391i | ||||||
\(590\) | −494.684 | − | 186.556i | −0.838447 | − | 0.316196i | ||||
\(591\) | 20.7713 | − | 11.9923i | 0.0351460 | − | 0.0202916i | ||||
\(592\) | −184.279 | + | 441.614i | −0.311282 | + | 0.745969i | ||||
\(593\) | −164.729 | − | 95.1064i | −0.277789 | − | 0.160382i | 0.354633 | − | 0.935006i | \(-0.384606\pi\) |
−0.632422 | + | 0.774624i | \(0.717939\pi\) | |||||||
\(594\) | 70.6647 | − | 11.6193i | 0.118964 | − | 0.0195610i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 39.4731 | + | 116.786i | 0.0662301 | + | 0.195950i | ||||
\(597\) | −67.8064 | − | 39.1480i | −0.113579 | − | 0.0655746i | ||||
\(598\) | 120.715 | − | 98.9360i | 0.201864 | − | 0.165445i | ||||
\(599\) | 146.832 | + | 254.320i | 0.245128 | + | 0.424574i | 0.962168 | − | 0.272458i | \(-0.0878366\pi\) |
−0.717040 | + | 0.697033i | \(0.754503\pi\) | |||||||
\(600\) | 24.7888 | + | 0.860245i | 0.0413146 | + | 0.00143374i | ||||
\(601\) | 597.574i | 0.994299i | 0.867665 | + | 0.497150i | \(0.165620\pi\) | ||||
−0.867665 | + | 0.497150i | \(0.834380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1121.31i | − | 1.85956i | ||||||
\(604\) | 18.4510 | − | 92.1287i | 0.0305480 | − | 0.152531i | ||||
\(605\) | −105.119 | − | 182.071i | −0.173750 | − | 0.300944i | ||||
\(606\) | 58.5060 | − | 47.9505i | 0.0965445 | − | 0.0791263i | ||||
\(607\) | 10.6620 | + | 6.15569i | 0.0175650 | + | 0.0101412i | 0.508757 | − | 0.860910i | \(-0.330105\pi\) |
−0.491192 | + | 0.871051i | \(0.663439\pi\) | |||||||
\(608\) | −577.881 | − | 544.807i | −0.950462 | − | 0.896064i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −58.6458 | − | 356.665i | −0.0961407 | − | 0.584697i | ||||
\(611\) | 799.512 | + | 461.599i | 1.30853 | + | 0.755481i | ||||
\(612\) | 225.165 | − | 256.075i | 0.367917 | − | 0.418422i | ||||
\(613\) | 118.897 | − | 68.6451i | 0.193959 | − | 0.111982i | −0.399876 | − | 0.916569i | \(-0.630947\pi\) |
0.593835 | + | 0.804587i | \(0.297613\pi\) | |||||||
\(614\) | 142.607 | + | 53.7800i | 0.232258 | + | 0.0875895i | ||||
\(615\) | 40.9416i | 0.0665717i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 290.516 | 0.470853 | 0.235427 | − | 0.971892i | \(-0.424351\pi\) | ||||
0.235427 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(618\) | 3.54656 | − | 9.40430i | 0.00573877 | − | 0.0152173i | ||||
\(619\) | −51.1586 | − | 88.6092i | −0.0826471 | − | 0.143149i | 0.821739 | − | 0.569864i | \(-0.193004\pi\) |
−0.904386 | + | 0.426715i | \(0.859671\pi\) | |||||||
\(620\) | −307.607 | + | 349.833i | −0.496140 | + | 0.564247i | ||||
\(621\) | 9.76379 | − | 16.9114i | 0.0157227 | − | 0.0272325i | ||||
\(622\) | −390.938 | + | 64.2812i | −0.628517 | + | 0.103346i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 58.4740 | − | 44.6259i | 0.0937083 | − | 0.0715158i | ||||
\(625\) | 84.5320 | − | 146.414i | 0.135251 | − | 0.234262i | ||||
\(626\) | −70.2222 | − | 85.6804i | −0.112176 | − | 0.136870i | ||||
\(627\) | −42.9098 | + | 24.7740i | −0.0684366 | + | 0.0395119i | ||||
\(628\) | −100.253 | + | 500.577i | −0.159638 | + | 0.797097i | ||||
\(629\) | 285.315 | 0.453600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −562.739 | −0.891820 | −0.445910 | − | 0.895078i | \(-0.647120\pi\) | ||||
−0.445910 | + | 0.895078i | \(0.647120\pi\) | |||||||
\(632\) | −824.112 | − | 28.5992i | −1.30397 | − | 0.0452519i | ||||
\(633\) | 27.6054 | − | 15.9380i | 0.0436104 | − | 0.0251785i | ||||
\(634\) | 379.268 | + | 462.757i | 0.598214 | + | 0.729900i | ||||
\(635\) | 102.893 | − | 178.216i | 0.162036 | − | 0.280655i | ||||
\(636\) | −20.3729 | − | 60.2758i | −0.0320328 | − | 0.0947732i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −72.5519 | − | 441.237i | −0.113718 | − | 0.691595i | ||||
\(639\) | −23.8508 | + | 41.3108i | −0.0373252 | + | 0.0646492i | ||||
\(640\) | 42.7265 | + | 455.187i | 0.0667602 | + | 0.711229i | ||||
\(641\) | 376.275 | + | 651.727i | 0.587012 | + | 1.01673i | 0.994621 | + | 0.103578i | \(0.0330291\pi\) |
−0.407610 | + | 0.913156i | \(0.633638\pi\) | |||||||
\(642\) | 1.63427 | − | 4.33353i | 0.00254558 | − | 0.00675005i | ||||
\(643\) | 253.143 | 0.393690 | 0.196845 | − | 0.980435i | \(-0.436930\pi\) | ||||
0.196845 | + | 0.980435i | \(0.436930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.5337i | 0.0349360i | ||||||||
\(646\) | −167.095 | + | 443.079i | −0.258660 | + | 0.685881i | ||||
\(647\) | −485.492 | + | 280.299i | −0.750374 | + | 0.433229i | −0.825829 | − | 0.563921i | \(-0.809292\pi\) |
0.0754551 | + | 0.997149i | \(0.475959\pi\) | |||||||
\(648\) | −335.947 | + | 537.887i | −0.518436 | + | 0.830073i | ||||
\(649\) | 505.244 | + | 291.703i | 0.778497 | + | 0.449465i | ||||
\(650\) | 72.1150 | + | 438.581i | 0.110946 | + | 0.674739i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −204.523 | − | 605.108i | −0.313686 | − | 0.928079i | ||||
\(653\) | 602.396 | + | 347.793i | 0.922505 | + | 0.532609i | 0.884433 | − | 0.466666i | \(-0.154545\pi\) |
0.0380717 | + | 0.999275i | \(0.487878\pi\) | |||||||
\(654\) | 38.2712 | + | 46.6959i | 0.0585186 | + | 0.0714004i | ||||
\(655\) | 221.985 | + | 384.489i | 0.338908 | + | 0.587007i | ||||
\(656\) | 718.219 | − | 92.6424i | 1.09485 | − | 0.141223i | ||||
\(657\) | − | 244.097i | − | 0.371533i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 323.387i | − | 0.490724i | −0.969432 | − | 0.245362i | \(-0.921093\pi\) | ||
0.969432 | − | 0.245362i | \(-0.0789068\pi\) | |||||||
\(660\) | 27.9671 | + | 5.60109i | 0.0423745 | + | 0.00848650i | ||||
\(661\) | −15.5168 | − | 26.8758i | −0.0234747 | − | 0.0406593i | 0.854049 | − | 0.520192i | \(-0.174140\pi\) |
−0.877524 | + | 0.479533i | \(0.840806\pi\) | |||||||
\(662\) | −475.894 | − | 580.654i | −0.718873 | − | 0.877120i | ||||
\(663\) | −37.9822 | − | 21.9291i | −0.0572884 | − | 0.0330755i | ||||
\(664\) | −193.763 | − | 364.223i | −0.291811 | − | 0.548529i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −527.416 | + | 86.7221i | −0.791916 | + | 0.130213i | ||||
\(667\) | −105.596 | − | 60.9661i | −0.158315 | − | 0.0914035i | ||||
\(668\) | −377.159 | + | 428.933i | −0.564610 | + | 0.642116i | ||||
\(669\) | 1.96213 | − | 1.13284i | 0.00293293 | − | 0.00169333i | ||||
\(670\) | 316.308 | − | 838.745i | 0.472102 | − | 1.25186i | ||||
\(671\) | 398.862i | 0.594429i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1011.75 | 1.50334 | 0.751670 | − | 0.659539i | \(-0.229249\pi\) | ||||
0.751670 | + | 0.659539i | \(0.229249\pi\) | |||||||
\(674\) | 9.33884 | + | 3.52187i | 0.0138558 | + | 0.00522533i | ||||
\(675\) | 27.8047 | + | 48.1592i | 0.0411922 | + | 0.0713469i | ||||
\(676\) | 482.210 | + | 424.005i | 0.713328 | + | 0.627227i | ||||
\(677\) | 34.7377 | − | 60.1674i | 0.0513112 | − | 0.0888736i | −0.839229 | − | 0.543778i | \(-0.816993\pi\) |
0.890540 | + | 0.454905i | \(0.150327\pi\) | |||||||
\(678\) | 10.1914 | + | 61.9806i | 0.0150315 | + | 0.0914169i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 240.660 | − | 128.028i | 0.353911 | − | 0.188277i | ||||
\(681\) | 34.5307 | − | 59.8089i | 0.0507058 | − | 0.0878251i | ||||
\(682\) | 397.578 | − | 325.848i | 0.582959 | − | 0.477784i | ||||
\(683\) | −824.530 | + | 476.042i | −1.20722 | + | 0.696987i | −0.962150 | − | 0.272519i | \(-0.912143\pi\) |
−0.245067 | + | 0.969506i | \(0.578810\pi\) | |||||||
\(684\) | 174.206 | − | 869.840i | 0.254688 | − | 1.27170i | ||||
\(685\) | −605.348 | −0.883720 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 83.8839 | 0.122102 | ||||||||
\(688\) | 395.299 | − | 50.9893i | 0.574563 | − | 0.0741123i | ||||
\(689\) | 987.391 | − | 570.070i | 1.43308 | − | 0.827388i | ||||
\(690\) | 6.01533 | − | 4.93007i | 0.00871787 | − | 0.00714502i | ||||
\(691\) | 34.0754 | − | 59.0204i | 0.0493132 | − | 0.0854130i | −0.840315 | − | 0.542098i | \(-0.817630\pi\) |
0.889628 | + | 0.456685i | \(0.150963\pi\) | |||||||
\(692\) | −741.888 | + | 250.754i | −1.07209 | + | 0.362361i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 730.975 | − | 120.193i | 1.05328 | − | 0.173189i | ||||
\(695\) | −475.935 | + | 824.343i | −0.684798 | + | 1.18611i | ||||
\(696\) | −48.7395 | − | 30.4411i | −0.0700281 | − | 0.0437372i | ||||
\(697\) | −215.891 | − | 373.934i | −0.309743 | − | 0.536490i | ||||
\(698\) | 48.0565 | + | 18.1231i | 0.0688489 | + | 0.0259644i | ||||
\(699\) | −40.0745 | −0.0573311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.67276i | 0.00238625i | 0.999999 | + | 0.00119312i | \(0.000379783\pi\) | ||||
−0.999999 | + | 0.00119312i | \(0.999620\pi\) | |||||||
\(702\) | 154.306 | + | 58.1921i | 0.219809 | + | 0.0828947i | ||||
\(703\) | 642.825 | − | 371.135i | 0.914403 | − | 0.527931i | ||||
\(704\) | 34.9734 | − | 503.289i | 0.0496781 | − | 0.714899i | ||||
\(705\) | 39.8404 | + | 23.0019i | 0.0565112 | + | 0.0326267i | ||||
\(706\) | −523.984 | + | 86.1577i | −0.742186 | + | 0.122036i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 71.0261 | − | 24.0064i | 0.100319 | − | 0.0339074i | ||||
\(709\) | 45.7969 | + | 26.4408i | 0.0645936 | + | 0.0372931i | 0.531949 | − | 0.846776i | \(-0.321460\pi\) |
−0.467355 | + | 0.884070i | \(0.654793\pi\) | |||||||
\(710\) | −29.4937 | + | 24.1726i | −0.0415405 | + | 0.0340459i | ||||
\(711\) | −460.536 | − | 797.673i | −0.647731 | − | 1.12190i | ||||
\(712\) | −42.6817 | + | 1229.91i | −0.0599461 | + | 1.72740i | ||||
\(713\) | − | 140.171i | − | 0.196593i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 511.109i | 0.714838i | ||||||||
\(716\) | 586.384 | + | 117.437i | 0.818972 | + | 0.164019i | ||||
\(717\) | 6.20454 | + | 10.7466i | 0.00865347 | + | 0.0149882i | ||||
\(718\) | −851.473 | + | 697.853i | −1.18590 | + | 0.971941i | ||||
\(719\) | 824.178 | + | 475.840i | 1.14628 | + | 0.661808i | 0.947979 | − | 0.318333i | \(-0.103123\pi\) |
0.198305 | + | 0.980140i | \(0.436456\pi\) | |||||||
\(720\) | −405.955 | + | 309.815i | −0.563827 | + | 0.430298i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 82.7399 | + | 503.198i | 0.114598 | + | 0.696950i | ||||
\(723\) | −43.2849 | − | 24.9906i | −0.0598685 | − | 0.0345651i | ||||
\(724\) | −274.255 | − | 241.151i | −0.378805 | − | 0.333081i | ||||
\(725\) | 300.711 | − | 173.615i | 0.414774 | − | 0.239470i | ||||
\(726\) | 27.8959 | + | 10.5201i | 0.0384241 | + | 0.0144905i | ||||
\(727\) | − | 1061.98i | − | 1.46078i | −0.683032 | − | 0.730388i | \(-0.739339\pi\) | ||
0.683032 | − | 0.730388i | \(-0.260661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −698.013 | −0.957494 | ||||||||
\(730\) | 68.8569 | − | 182.586i | 0.0943245 | − | 0.250117i | ||||
\(731\) | −118.824 | − | 205.809i | −0.162550 | − | 0.281544i | ||||
\(732\) | 38.4933 | + | 33.8470i | 0.0525865 | + | 0.0462391i | ||||
\(733\) | 0.148102 | − | 0.256519i | 0.000202048 | − | 0.000349958i | −0.865924 | − | 0.500175i | \(-0.833269\pi\) |
0.866126 | + | 0.499825i | \(0.166602\pi\) | |||||||
\(734\) | 410.409 | − | 67.4828i | 0.559140 | − | 0.0919384i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −100.097 | − | 94.3684i | −0.136002 | − | 0.128218i | ||||
\(737\) | −494.588 | + | 856.651i | −0.671082 | + | 1.16235i | ||||
\(738\) | 512.741 | + | 625.612i | 0.694772 | + | 0.847713i | ||||
\(739\) | 176.276 | − | 101.773i | 0.238533 | − | 0.137717i | −0.375969 | − | 0.926632i | \(-0.622690\pi\) |
0.614502 | + | 0.788915i | \(0.289357\pi\) | |||||||
\(740\) | −418.972 | − | 83.9092i | −0.566178 | − | 0.113391i | ||||
\(741\) | −114.101 | −0.153982 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1142.13 | 1.53718 | 0.768592 | − | 0.639739i | \(-0.220958\pi\) | ||||
0.768592 | + | 0.639739i | \(0.220958\pi\) | |||||||
\(744\) | 2.29111 | − | 66.0205i | 0.00307945 | − | 0.0887373i | ||||
\(745\) | −95.3315 | + | 55.0397i | −0.127962 | + | 0.0738788i | ||||
\(746\) | −576.102 | − | 702.920i | −0.772255 | − | 0.942253i | ||||
\(747\) | 230.409 | − | 399.080i | 0.308446 | − | 0.534244i | ||||
\(748\) | −284.969 | + | 96.3180i | −0.380975 | + | 0.128767i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.9319 | + | 66.4843i | 0.0145759 | + | 0.0886457i | ||||
\(751\) | 396.068 | − | 686.010i | 0.527387 | − | 0.913462i | −0.472103 | − | 0.881543i | \(-0.656505\pi\) |
0.999490 | − | 0.0319185i | \(-0.0101617\pi\) | |||||||
\(752\) | 313.360 | − | 750.950i | 0.416702 | − | 0.998604i | ||||
\(753\) | −39.9508 | − | 69.1967i | −0.0530554 | − | 0.0918947i | ||||
\(754\) | 363.357 | − | 963.503i | 0.481906 | − | 1.27786i | ||||
\(755\) | 83.8995 | 0.111125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1179.34i | − | 1.55792i | −0.627076 | − | 0.778958i | \(-0.715748\pi\) | ||
0.627076 | − | 0.778958i | \(-0.284252\pi\) | |||||||
\(758\) | 263.408 | − | 698.470i | 0.347504 | − | 0.921465i | ||||
\(759\) | −7.43259 | + | 4.29121i | −0.00979260 | + | 0.00565376i | ||||
\(760\) | 375.678 | − | 601.501i | 0.494313 | − | 0.791449i | ||||
\(761\) | −197.869 | − | 114.240i | −0.260011 | − | 0.150118i | 0.364328 | − | 0.931271i | \(-0.381299\pi\) |
−0.624340 | + | 0.781153i | \(0.714632\pi\) | |||||||
\(762\) | 4.73482 | + | 28.7957i | 0.00621368 | + | 0.0377896i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −105.451 | + | 35.6420i | −0.138025 | + | 0.0466518i | ||||
\(765\) | 263.691 | + | 152.242i | 0.344694 | + | 0.199009i | ||||
\(766\) | −395.689 | − | 482.792i | −0.516565 | − | 0.630277i | ||||
\(767\) | 671.744 | + | 1163.49i | 0.875807 | + | 1.51694i | ||||
\(768\) | −45.6035 | − | 46.0837i | −0.0593795 | − | 0.0600049i | ||||
\(769\) | − | 83.4232i | − | 0.108483i | −0.998528 | − | 0.0542414i | \(-0.982726\pi\) | ||
0.998528 | − | 0.0542414i | \(-0.0172740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 96.3670i | 0.124990i | ||||||||
\(772\) | 190.392 | − | 950.658i | 0.246622 | − | 1.23142i | ||||
\(773\) | 285.318 | + | 494.186i | 0.369105 | + | 0.639309i | 0.989426 | − | 0.145039i | \(-0.0463309\pi\) |
−0.620321 | + | 0.784348i | \(0.712998\pi\) | |||||||
\(774\) | 282.207 | + | 344.329i | 0.364608 | + | 0.444870i | ||||
\(775\) | 345.691 | + | 199.585i | 0.446052 | + | 0.257528i | ||||
\(776\) | 332.258 | − | 176.757i | 0.428168 | − | 0.227780i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1001.83 | + | 164.728i | −1.28769 | + | 0.211733i | ||||
\(779\) | −972.822 | − | 561.659i | −1.24881 | − | 0.721000i | ||||
\(780\) | 49.3261 | + | 43.3722i | 0.0632385 | + | 0.0556054i | ||||
\(781\) | 36.4427 | − | 21.0402i | 0.0466616 | − | 0.0269401i | ||||
\(782\) | −28.9432 | + | 76.7477i | −0.0370117 | + | 0.0981429i | ||||
\(783\) | − | 128.835i | − | 0.164540i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −455.864 | −0.580718 | ||||||||
\(786\) | −58.9093 | − | 22.2159i | −0.0749482 | − | 0.0282645i | ||||
\(787\) | −382.719 | − | 662.888i | −0.486301 | − | 0.842298i | 0.513575 | − | 0.858045i | \(-0.328321\pi\) |
−0.999876 | + | 0.0157470i | \(0.994987\pi\) | |||||||
\(788\) | 250.146 | − | 284.485i | 0.317444 | − | 0.361021i | ||||
\(789\) | 24.8605 | − | 43.0597i | 0.0315089 | − | 0.0545750i | ||||
\(790\) | −119.469 | − | 726.573i | −0.151227 | − | 0.919713i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 497.501 | − | 264.665i | 0.628158 | − | 0.334173i | ||||
\(793\) | −459.257 | + | 795.456i | −0.579138 | + | 1.00310i | ||||
\(794\) | −295.909 | + | 242.522i | −0.372681 | + | 0.305443i | ||||
\(795\) | 49.2025 | − | 28.4071i | 0.0618900 | − | 0.0357322i | ||||
\(796\) | −1212.55 | − | 242.843i | −1.52331 | − | 0.305079i | ||||
\(797\) | −577.729 | −0.724880 | −0.362440 | − | 0.932007i | \(-0.618056\pi\) | ||||
−0.362440 | + | 0.932007i | \(0.618056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −485.168 | −0.607220 | ||||||||
\(800\) | 375.258 | − | 112.493i | 0.469072 | − | 0.140616i | ||||
\(801\) | −1190.45 | + | 687.309i | −1.48621 | + | 0.858063i | ||||
\(802\) | −189.338 | + | 155.178i | −0.236082 | + | 0.193489i | ||||
\(803\) | −107.666 | + | 186.484i | −0.134080 | + | 0.232234i | ||||
\(804\) | 40.7033 | + | 120.426i | 0.0506260 | + | 0.149784i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1168.08 | − | 192.066i | 1.44923 | − | 0.238295i | ||||
\(807\) | 12.9555 | − | 22.4396i | 0.0160539 | − | 0.0278062i | ||||
\(808\) | 632.908 | − | 1013.35i | 0.783301 | − | 1.25415i | ||||
\(809\) | 41.4824 | + | 71.8496i | 0.0512761 | + | 0.0888128i | 0.890524 | − | 0.454936i | \(-0.150338\pi\) |
−0.839248 | + | 0.543749i | \(0.817004\pi\) | |||||||
\(810\) | −529.860 | − | 199.822i | −0.654149 | − | 0.246693i | ||||
\(811\) | 525.164 | 0.647552 | 0.323776 | − | 0.946134i | \(-0.395048\pi\) | ||||
0.323776 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.9150i | 0.0798462i | ||||||||
\(814\) | 441.182 | + | 166.379i | 0.541993 | + | 0.204397i | ||||
\(815\) | 493.944 | − | 285.178i | 0.606066 | − | 0.349912i | ||||
\(816\) | −14.8867 | + | 35.6752i | −0.0182435 | + | 0.0437196i | ||||
\(817\) | −535.429 | − | 309.130i | −0.655360 | − | 0.378372i | ||||
\(818\) | −10.4311 | + | 1.71516i | −0.0127519 | + | 0.00209677i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 207.055 | + | 612.598i | 0.252506 | + | 0.747070i | ||||
\(821\) | −506.369 | − | 292.352i | −0.616771 | − | 0.356093i | 0.158840 | − | 0.987304i | \(-0.449225\pi\) |
−0.775611 | + | 0.631211i | \(0.782558\pi\) | |||||||
\(822\) | 66.3940 | − | 54.4155i | 0.0807713 | − | 0.0661989i | ||||
\(823\) | −590.484 | − | 1022.75i | −0.717478 | − | 1.24271i | −0.961996 | − | 0.273063i | \(-0.911963\pi\) |
0.244518 | − | 0.969645i | \(-0.421370\pi\) | |||||||
\(824\) | 5.50564 | − | 158.650i | 0.00668160 | − | 0.192537i | ||||
\(825\) | − | 24.4405i | − | 0.0296248i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 336.806i | − | 0.407262i | −0.979048 | − | 0.203631i | \(-0.934726\pi\) | ||
0.979048 | − | 0.203631i | \(-0.0652743\pi\) | |||||||
\(828\) | 30.1750 | − | 150.669i | 0.0364433 | − | 0.181967i | ||||
\(829\) | −184.145 | − | 318.949i | −0.222130 | − | 0.384740i | 0.733325 | − | 0.679878i | \(-0.237967\pi\) |
−0.955454 | + | 0.295139i | \(0.904634\pi\) | |||||||
\(830\) | 284.922 | − | 233.518i | 0.343280 | − | 0.281346i | ||||
\(831\) | −43.1479 | − | 24.9114i | −0.0519228 | − | 0.0299777i | ||||
\(832\) | 649.243 | − | 963.446i | 0.780340 | − | 1.15799i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.9011 | − | 133.196i | −0.0262603 | − | 0.159707i | ||||
\(835\) | −441.692 | − | 255.011i | −0.528972 | − | 0.305402i | ||||
\(836\) | −516.757 | + | 587.694i | −0.618131 | + | 0.702984i | ||||
\(837\) | 128.264 | − | 74.0530i | 0.153242 | − | 0.0884743i | ||||
\(838\) | −64.9658 | − | 24.5000i | −0.0775249 | − | 0.0292363i | ||||
\(839\) | 709.889i | 0.846113i | 0.906103 | + | 0.423056i | \(0.139043\pi\) | ||||
−0.906103 | + | 0.423056i | \(0.860957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.5402 | 0.0434485 | ||||||||
\(842\) | −278.294 | + | 737.943i | −0.330515 | + | 0.876417i | ||||
\(843\) | −8.90098 | − | 15.4169i | −0.0105587 | − | 0.0182882i | ||||
\(844\) | 332.448 | − | 378.084i | 0.393896 | − | 0.447967i | ||||
\(845\) | −286.685 | + | 496.553i | −0.339272 | + | 0.587637i | ||||
\(846\) | 896.854 | − | 147.468i | 1.06011 | − | 0.174312i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −609.668 | − | 798.858i | −0.718948 | − | 0.942049i | ||||
\(849\) | −37.6073 | + | 65.1377i | −0.0442960 | + | 0.0767229i | ||||
\(850\) | −148.065 | − | 180.659i | −0.174194 | − | 0.212540i | ||||
\(851\) | 111.347 | − | 64.2860i | 0.130842 | − | 0.0755417i | ||||
\(852\) | 1.06194 | − | 5.30246i | 0.00124641 | − | 0.00622354i | ||||
\(853\) | −1136.65 | −1.33253 | −0.666267 | − | 0.745713i | \(-0.732109\pi\) | ||||
−0.666267 | + | 0.745713i | \(0.732109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 792.143 | 0.926483 | ||||||||
\(856\) | 2.53701 | − | 73.1064i | 0.00296380 | − | 0.0854047i | ||||
\(857\) | −578.645 | + | 334.081i | −0.675198 | + | 0.389826i | −0.798043 | − | 0.602600i | \(-0.794131\pi\) |
0.122845 | + | 0.992426i | \(0.460798\pi\) | |||||||
\(858\) | −45.9442 | − | 56.0580i | −0.0535480 | − | 0.0653357i | ||||
\(859\) | −100.378 | + | 173.859i | −0.116854 | + | 0.202397i | −0.918519 | − | 0.395376i | \(-0.870614\pi\) |
0.801665 | + | 0.597773i | \(0.203948\pi\) | |||||||
\(860\) | 113.960 | + | 337.166i | 0.132512 | + | 0.392054i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −140.100 | − | 852.045i | −0.162529 | − | 0.988451i | ||||
\(863\) | −21.7855 | + | 37.7337i | −0.0252440 | + | 0.0437238i | −0.878371 | − | 0.477979i | \(-0.841370\pi\) |
0.853127 | + | 0.521703i | \(0.174703\pi\) | |||||||
\(864\) | 33.4701 | − | 141.450i | 0.0387385 | − | 0.163715i | ||||
\(865\) | −349.641 | − | 605.596i | −0.404209 | − | 0.700111i | ||||
\(866\) | −224.798 | + | 596.091i | −0.259582 | + | 0.688326i | ||||
\(867\) | −50.1422 | −0.0578342 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 812.533i | 0.935020i | ||||||||
\(870\) | 18.1064 | − | 48.0122i | 0.0208120 | − | 0.0551864i | ||||
\(871\) | −1972.73 | + | 1138.95i | −2.26490 | + | 1.30764i | ||||
\(872\) | 808.797 | + | 505.148i | 0.927520 | + | 0.579298i | ||||
\(873\) | 364.056 | + | 210.188i | 0.417017 | + | 0.240765i | ||||
\(874\) | 34.6228 | + | 210.565i | 0.0396142 | + | 0.240921i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.86068 | + | 26.2154i | 0.0101149 | + | 0.0299263i | ||||
\(877\) | −129.242 | − | 74.6180i | −0.147368 | − | 0.0850832i | 0.424503 | − | 0.905427i | \(-0.360449\pi\) |
−0.571871 | + | 0.820343i | \(0.693782\pi\) | |||||||
\(878\) | 779.964 | + | 951.659i | 0.888342 | + | 1.08389i | ||||
\(879\) | −17.1658 | − | 29.7321i | −0.0195288 | − | 0.0338249i | ||||
\(880\) | 446.791 | − | 57.6312i | 0.507717 | − | 0.0654900i | ||||
\(881\) | 865.257i | 0.982130i | 0.871123 | + | 0.491065i | \(0.163392\pi\) | ||||
−0.871123 | + | 0.491065i | \(0.836608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1476.24i | 1.67184i | 0.548850 | + | 0.835921i | \(0.315066\pi\) | ||||
−0.548850 | + | 0.835921i | \(0.684934\pi\) | |||||||
\(884\) | −679.220 | − | 136.030i | −0.768348 | − | 0.153880i | ||||
\(885\) | 33.4736 | + | 57.9779i | 0.0378233 | + | 0.0655118i | ||||
\(886\) | 126.562 | + | 154.422i | 0.142846 | + | 0.174291i | ||||
\(887\) | 518.166 | + | 299.163i | 0.584178 | + | 0.337275i | 0.762792 | − | 0.646644i | \(-0.223828\pi\) |
−0.178614 | + | 0.983919i | \(0.557161\pi\) | |||||||
\(888\) | 53.4951 | − | 28.4588i | 0.0602423 | − | 0.0320482i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1084.34 | + | 178.297i | −1.21836 | + | 0.200333i | ||||
\(891\) | 541.172 | + | 312.446i | 0.607376 | + | 0.350669i | ||||
\(892\) | 23.6297 | − | 26.8735i | 0.0264907 | − | 0.0301272i | ||||
\(893\) | −1093.10 | + | 631.104i | −1.22408 | + | 0.706723i | ||||
\(894\) | 5.50829 | − | 14.6062i | 0.00616140 | − | 0.0163380i | ||||
\(895\) | 534.006i | 0.596655i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.7639 | −0.0220333 | ||||||||
\(898\) | 140.944 | + | 53.1530i | 0.156953 | + | 0.0591904i | ||||
\(899\) | −462.395 | − | 800.891i | −0.514343 | − | 0.890869i | ||||
\(900\) | 328.616 | + | 288.951i | 0.365129 | + | 0.321056i | ||||
\(901\) | −299.589 | + | 518.904i | −0.332508 | + | 0.575920i | ||||
\(902\) | −115.775 | − | 704.110i | −0.128354 | − | 0.780609i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 465.946 | + | 875.858i | 0.515428 | + | 0.968870i | ||||
\(905\) | 163.051 | − | 282.412i | 0.180167 | − | 0.312058i | ||||
\(906\) | −9.20202 | + | 7.54182i | −0.0101568 | + | 0.00832431i | ||||
\(907\) | 1463.00 | − | 844.666i | 1.61301 | − | 0.931274i | 0.624348 | − | 0.781146i | \(-0.285365\pi\) |
0.988667 | − | 0.150128i | \(-0.0479687\pi\) | |||||||
\(908\) | 214.200 | − | 1069.54i | 0.235904 | − | 1.17790i | ||||
\(909\) | 1334.53 | 1.46813 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −813.339 | −0.892798 | −0.446399 | − | 0.894834i | \(-0.647294\pi\) | ||||
−0.446399 | + | 0.894834i | \(0.647294\pi\) | |||||||
\(912\) | 12.8657 | + | 99.7422i | 0.0141071 | + | 0.109366i | ||||
\(913\) | −352.052 | + | 203.257i | −0.385599 | + | 0.222626i | ||||
\(914\) | −323.127 | + | 264.830i | −0.353531 | + | 0.289748i | ||||
\(915\) | −22.8852 | + | 39.6382i | −0.0250111 | + | 0.0433205i | ||||
\(916\) | 1255.13 | − | 424.228i | 1.37023 | − | 0.463131i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −85.5191 | + | 14.0617i | −0.0931581 | + | 0.0153178i | ||||
\(919\) | −751.489 | + | 1301.62i | −0.817724 | + | 1.41634i | 0.0896310 | + | 0.995975i | \(0.471431\pi\) |
−0.907355 | + | 0.420365i | \(0.861902\pi\) | |||||||
\(920\) | 65.0728 | − | 104.189i | 0.0707313 | − | 0.113249i | ||||
\(921\) | −9.64971 | − | 16.7138i | −0.0104774 | − | 0.0181474i | ||||
\(922\) | −1406.25 | − | 530.325i | −1.52521 | − | 0.575190i | ||||
\(923\) | 96.9043 | 0.104988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 366.139i | 0.395826i | ||||||||
\(926\) | 6.66340 | + | 2.51291i | 0.00719590 | + | 0.00271373i | ||||
\(927\) | 153.560 | − | 88.6581i | 0.165653 | − | 0.0956398i | ||||
\(928\) | −883.227 | − | 208.991i | −0.951753 | − | 0.225205i | ||||
\(929\) | 1301.71 | + | 751.543i | 1.40120 | + | 0.808981i | 0.994515 | − | 0.104589i | \(-0.0333528\pi\) |
0.406681 | + | 0.913570i | \(0.366686\pi\) | |||||||
\(930\) | 58.2066 | − | 9.57080i | 0.0625877 | − | 0.0102912i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −599.623 | + | 202.669i | −0.643373 | + | 0.217456i | ||||
\(933\) | 43.4471 | + | 25.0842i | 0.0465671 | + | 0.0268855i | ||||
\(934\) | 640.227 | − | 524.720i | 0.685468 | − | 0.561798i | ||||
\(935\) | −134.302 | − | 232.618i | −0.143638 | − | 0.248789i | ||||
\(936\) | 1296.91 | + | 45.0068i | 1.38559 | + | 0.0480842i | ||||
\(937\) | − | 419.349i | − | 0.447545i | −0.974641 | − | 0.223772i | \(-0.928163\pi\) | ||
0.974641 | − | 0.223772i | \(-0.0718372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0279i | 0.0149392i | ||||||||
\(940\) | 712.449 | + | 142.685i | 0.757924 | + | 0.151792i | ||||
\(941\) | 261.680 | + | 453.243i | 0.278087 | + | 0.481661i | 0.970909 | − | 0.239448i | \(-0.0769664\pi\) |
−0.692822 | + | 0.721108i | \(0.743633\pi\) | |||||||
\(942\) | 49.9987 | − | 40.9781i | 0.0530772 | − | 0.0435012i | ||||
\(943\) | −168.507 | − | 97.2874i | −0.178692 | − | 0.103168i | ||||
\(944\) | 941.336 | − | 718.404i | 0.997178 | − | 0.761021i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.7214 | − | 387.533i | −0.0673588 | − | 0.409655i | ||||
\(947\) | 311.949 | + | 180.104i | 0.329408 | + | 0.190184i | 0.655578 | − | 0.755127i | \(-0.272425\pi\) |
−0.326170 | + | 0.945311i | \(0.605758\pi\) | |||||||
\(948\) | 78.4157 | + | 68.9506i | 0.0827170 | + | 0.0727327i | ||||
\(949\) | −429.441 | + | 247.938i | −0.452520 | + | 0.261262i | ||||
\(950\) | −568.596 | − | 214.430i | −0.598522 | − | 0.225715i | ||||
\(951\) | − | 75.7642i | − | 0.0796679i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1242.81 | 1.30410 | 0.652051 | − | 0.758175i | \(-0.273909\pi\) | ||||
0.652051 | + | 0.758175i | \(0.273909\pi\) | |||||||
\(954\) | 396.081 | − | 1050.28i | 0.415180 | − | 1.10092i | ||||
\(955\) | −49.6976 | − | 86.0789i | −0.0520394 | − | 0.0901349i | ||||
\(956\) | 147.186 | + | 129.420i | 0.153960 | + | 0.135376i | ||||
\(957\) | −28.3116 | + | 49.0372i | −0.0295838 | + | 0.0512406i | ||||
\(958\) | −1790.68 | + | 294.438i | −1.86918 | + | 0.307346i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 32.3524 | − | 48.0094i | 0.0337004 | − | 0.0500098i | ||||
\(961\) | 51.0585 | − | 88.4359i | 0.0531306 | − | 0.0920248i | ||||
\(962\) | 688.284 | + | 839.797i | 0.715472 | + | 0.872970i | ||||
\(963\) | 70.7610 | − | 40.8539i | 0.0734798 | − | 0.0424236i | ||||
\(964\) | −774.046 | − | 155.021i | −0.802952 | − | 0.160810i | ||||
\(965\) | 865.742 | 0.897142 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 81.8793 | 0.0846735 | 0.0423368 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423368 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(968\) | 470.602 | + | 16.3313i | 0.486159 | + | 0.0168712i | ||||
\(969\) | 51.9298 | − | 29.9817i | 0.0535912 | − | 0.0309409i | ||||
\(970\) | 213.023 | + | 259.917i | 0.219612 | + | 0.267955i | ||||
\(971\) | 409.052 | − | 708.499i | 0.421269 | − | 0.729660i | −0.574795 | − | 0.818298i | \(-0.694918\pi\) |
0.996064 | + | 0.0886380i | \(0.0282514\pi\) | |||||||
\(972\) | 230.992 | − | 78.0742i | 0.237646 | − | 0.0803232i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 273.522 | + | 1663.47i | 0.280823 | + | 1.70788i | ||||
\(975\) | 28.1412 | − | 48.7419i | 0.0288627 | − | 0.0499917i | ||||
\(976\) | 747.140 | + | 311.770i | 0.765512 | + | 0.319437i | ||||
\(977\) | −448.155 | − | 776.227i | −0.458705 | − | 0.794500i | 0.540188 | − | 0.841544i | \(-0.318353\pi\) |
−0.998893 | + | 0.0470441i | \(0.985020\pi\) | |||||||
\(978\) | −28.5402 | + | 75.6793i | −0.0291823 | + | 0.0773817i | ||||
\(979\) | 1212.63 | 1.23864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1065.14i | 1.08577i | ||||||||
\(982\) | −101.713 | + | 269.710i | −0.103578 | + | 0.274654i | ||||
\(983\) | −852.404 | + | 492.136i | −0.867146 | + | 0.500647i | −0.866399 | − | 0.499353i | \(-0.833571\pi\) |
−0.000746983 | 1.00000i | \(0.500238\pi\) | ||||||||
\(984\) | −77.7767 | − | 48.5767i | −0.0790413 | − | 0.0493666i | ||||
\(985\) | 292.947 | + | 169.133i | 0.297408 | + | 0.171708i | ||||
\(986\) | 87.8030 | + | 533.990i | 0.0890497 | + | 0.541572i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1707.26 | + | 577.044i | −1.72799 | + | 0.584052i | ||||
\(989\) | −92.7440 | − | 53.5458i | −0.0937756 | − | 0.0541414i | ||||
\(990\) | 318.967 | + | 389.182i | 0.322189 | + | 0.393113i | ||||
\(991\) | 612.037 | + | 1060.08i | 0.617596 | + | 1.06971i | 0.989923 | + | 0.141606i | \(0.0452265\pi\) |
−0.372327 | + | 0.928101i | \(0.621440\pi\) | |||||||
\(992\) | −299.606 | − | 999.434i | −0.302022 | − | 1.00749i | ||||
\(993\) | 95.0667i | 0.0957368i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1104.24i | − | 1.10979i | ||||||
\(996\) | −10.2588 | + | 51.2240i | −0.0103000 | + | 0.0514297i | ||||
\(997\) | 186.825 | + | 323.590i | 0.187387 | + | 0.324563i | 0.944378 | − | 0.328861i | \(-0.106665\pi\) |
−0.756991 | + | 0.653425i | \(0.773332\pi\) | |||||||
\(998\) | −483.235 | − | 589.610i | −0.484203 | − | 0.590792i | ||||
\(999\) | 117.650 | + | 67.9254i | 0.117768 | + | 0.0679934i |
(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 | 392.3.j.e.117.2 | 28 | ||
7.2 | even | 3 | 392.3.h.a.293.15 | 28 | |||
7.3 | odd | 6 | inner | 392.3.j.e.325.12 | 28 | ||
7.4 | even | 3 | 56.3.j.a.45.12 | yes | 28 | ||
7.5 | odd | 6 | 392.3.h.a.293.16 | 28 | |||
7.6 | odd | 2 | 56.3.j.a.5.2 | ✓ | 28 | ||
8.5 | even | 2 | inner | 392.3.j.e.117.12 | 28 | ||
28.11 | odd | 6 | 224.3.n.a.17.7 | 28 | |||
28.19 | even | 6 | 1568.3.h.a.881.14 | 28 | |||
28.23 | odd | 6 | 1568.3.h.a.881.16 | 28 | |||
28.27 | even | 2 | 224.3.n.a.145.8 | 28 | |||
56.5 | odd | 6 | 392.3.h.a.293.13 | 28 | |||
56.11 | odd | 6 | 224.3.n.a.17.8 | 28 | |||
56.13 | odd | 2 | 56.3.j.a.5.12 | yes | 28 | ||
56.19 | even | 6 | 1568.3.h.a.881.15 | 28 | |||
56.27 | even | 2 | 224.3.n.a.145.7 | 28 | |||
56.37 | even | 6 | 392.3.h.a.293.14 | 28 | |||
56.45 | odd | 6 | inner | 392.3.j.e.325.2 | 28 | ||
56.51 | odd | 6 | 1568.3.h.a.881.13 | 28 | |||
56.53 | even | 6 | 56.3.j.a.45.2 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.2 | ✓ | 28 | 7.6 | odd | 2 | ||
56.3.j.a.5.12 | yes | 28 | 56.13 | odd | 2 | ||
56.3.j.a.45.2 | yes | 28 | 56.53 | even | 6 | ||
56.3.j.a.45.12 | yes | 28 | 7.4 | even | 3 | ||
224.3.n.a.17.7 | 28 | 28.11 | odd | 6 | |||
224.3.n.a.17.8 | 28 | 56.11 | odd | 6 | |||
224.3.n.a.145.7 | 28 | 56.27 | even | 2 | |||
224.3.n.a.145.8 | 28 | 28.27 | even | 2 | |||
392.3.h.a.293.13 | 28 | 56.5 | odd | 6 | |||
392.3.h.a.293.14 | 28 | 56.37 | even | 6 | |||
392.3.h.a.293.15 | 28 | 7.2 | even | 3 | |||
392.3.h.a.293.16 | 28 | 7.5 | odd | 6 | |||
392.3.j.e.117.2 | 28 | 1.1 | even | 1 | trivial | ||
392.3.j.e.117.12 | 28 | 8.5 | even | 2 | inner | ||
392.3.j.e.325.2 | 28 | 56.45 | odd | 6 | inner | ||
392.3.j.e.325.12 | 28 | 7.3 | odd | 6 | inner | ||
1568.3.h.a.881.13 | 28 | 56.51 | odd | 6 | |||
1568.3.h.a.881.14 | 28 | 28.19 | even | 6 | |||
1568.3.h.a.881.15 | 28 | 56.19 | even | 6 | |||
1568.3.h.a.881.16 | 28 | 28.23 | odd | 6 |