Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), 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: | \(51.9643576194\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.6.e.a.109.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −27.0000 | − | 46.7654i | −0.482991 | − | 0.836564i | 0.516819 | − | 0.856095i | \(-0.327116\pi\) |
−0.999809 | + | 0.0195305i | \(0.993783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.0000 | − | 76.2102i | 0.339397 | − | 0.587852i | −0.644923 | − | 0.764248i | \(-0.723110\pi\) |
0.984319 | + | 0.176396i | \(0.0564438\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −270.000 | + | 467.654i | −0.672794 | + | 1.16531i | 0.304315 | + | 0.952572i | \(0.401573\pi\) |
−0.977108 | + | 0.212742i | \(0.931761\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 209.000 | + | 361.999i | 0.342995 | + | 0.594085i | 0.984987 | − | 0.172626i | \(-0.0552252\pi\) |
−0.641992 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 594.000 | 0.498499 | 0.249249 | − | 0.968439i | \(-0.419816\pi\) | ||||
0.249249 | + | 0.968439i | \(0.419816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 836.000 | 0.531279 | 0.265639 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2052.00 | + | 3554.17i | 0.808831 | + | 1.40094i | 0.913674 | + | 0.406448i | \(0.133233\pi\) |
−0.104843 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.500 | − | 180.999i | 0.0334400 | − | 0.0579198i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 297.000 | − | 514.419i | 0.0655785 | − | 0.113585i | −0.831372 | − | 0.555716i | \(-0.812444\pi\) |
0.896950 | + | 0.442131i | \(0.145777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2128.00 | − | 3685.80i | −0.397711 | − | 0.688855i | 0.595732 | − | 0.803183i | \(-0.296862\pi\) |
−0.993443 | + | 0.114328i | \(0.963529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4752.00 | −0.655702 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −298.000 | −0.0357859 | −0.0178930 | − | 0.999840i | \(-0.505696\pi\) | ||||
−0.0178930 | + | 0.999840i | \(0.505696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8613.00 | − | 14918.2i | −0.800193 | − | 1.38598i | −0.919489 | − | 0.393116i | \(-0.871397\pi\) |
0.119296 | − | 0.992859i | \(-0.461936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6050.00 | − | 10478.9i | 0.498981 | − | 0.864261i | −0.501018 | − | 0.865437i | \(-0.667041\pi\) |
0.999999 | + | 0.00117594i | \(0.000374313\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 648.000 | − | 1122.37i | 0.0427888 | − | 0.0741124i | −0.843838 | − | 0.536598i | \(-0.819709\pi\) |
0.886627 | + | 0.462486i | \(0.153042\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4531.50 | + | 7848.79i | 0.269620 | + | 0.466995i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19494.0 | 0.953260 | 0.476630 | − | 0.879104i | \(-0.341858\pi\) | ||||
0.476630 | + | 0.879104i | \(0.341858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29160.0 | 1.29981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3834.00 | + | 6640.68i | 0.143391 | + | 0.248361i | 0.928772 | − | 0.370653i | \(-0.120866\pi\) |
−0.785380 | + | 0.619013i | \(0.787533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17369.0 | − | 30084.0i | 0.597655 | − | 1.03517i | −0.395512 | − | 0.918461i | \(-0.629433\pi\) |
0.993166 | − | 0.116707i | \(-0.0372339\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11286.0 | − | 19547.9i | 0.331327 | − | 0.573875i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10906.0 | − | 18889.7i | −0.296810 | − | 0.514090i | 0.678594 | − | 0.734513i | \(-0.262589\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −46872.0 | −1.10349 | −0.551744 | − | 0.834014i | \(-0.686037\pi\) | ||||
−0.551744 | + | 0.834014i | \(0.686037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 67562.0 | 1.48387 | 0.741934 | − | 0.670473i | \(-0.233909\pi\) | ||||
0.741934 | + | 0.670473i | \(0.233909\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23760.0 | + | 41153.5i | 0.456688 | + | 0.791007i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38456.0 | − | 66607.7i | 0.693260 | − | 1.20076i | −0.277503 | − | 0.960725i | \(-0.589507\pi\) |
0.970764 | − | 0.240037i | \(-0.0771597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −33858.0 | + | 58643.8i | −0.539468 | + | 0.934387i | 0.459464 | + | 0.888196i | \(0.348041\pi\) |
−0.998933 | + | 0.0461905i | \(0.985292\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16038.0 | − | 27778.6i | −0.240770 | − | 0.417026i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 29754.0 | 0.398172 | 0.199086 | − | 0.979982i | \(-0.436203\pi\) | ||||
0.199086 | + | 0.979982i | \(0.436203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36784.0 | 0.465646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22572.0 | − | 39095.9i | −0.256603 | − | 0.444449i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61199.0 | − | 106000.i | 0.660412 | − | 1.14387i | −0.320095 | − | 0.947385i | \(-0.603715\pi\) |
0.980507 | − | 0.196482i | \(-0.0629517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5643.00 | + | 9773.96i | −0.0550436 | + | 0.0953383i | −0.892234 | − | 0.451573i | \(-0.850863\pi\) |
0.837191 | + | 0.546911i | \(0.184196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13628.0 | + | 23604.4i | 0.126572 | + | 0.219230i | 0.922346 | − | 0.386364i | \(-0.126269\pi\) |
−0.795774 | + | 0.605594i | \(0.792936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 122364. | 1.03322 | 0.516612 | − | 0.856220i | \(-0.327193\pi\) | ||||
0.516612 | + | 0.856220i | \(0.327193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 99902.0 | 0.805393 | 0.402697 | − | 0.915334i | \(-0.368073\pi\) | ||||
0.402697 | + | 0.915334i | \(0.368073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14823.0 | + | 25674.2i | 0.109204 | + | 0.189148i | 0.915448 | − | 0.402436i | \(-0.131836\pi\) |
−0.806244 | + | 0.591583i | \(0.798503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 110808. | − | 191925.i | 0.781316 | − | 1.35328i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26136.0 | − | 45268.9i | 0.169189 | − | 0.293044i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −65274.5 | − | 113059.i | −0.405303 | − | 0.702006i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −180036. | −1.03059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 336512. | 1.85136 | 0.925681 | − | 0.378305i | \(-0.123493\pi\) | ||||
0.925681 | + | 0.378305i | \(0.123493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50490.0 | − | 87451.2i | −0.257056 | − | 0.445233i | 0.708396 | − | 0.705815i | \(-0.249419\pi\) |
−0.965452 | + | 0.260582i | \(0.916086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36784.0 | − | 63711.8i | 0.180314 | − | 0.312313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 158571. | − | 274653.i | 0.721809 | − | 1.25021i | −0.238465 | − | 0.971151i | \(-0.576644\pi\) |
0.960274 | − | 0.279059i | \(-0.0900225\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 74162.0 | + | 128452.i | 0.325570 | + | 0.563904i | 0.981628 | − | 0.190807i | \(-0.0611105\pi\) |
−0.656058 | + | 0.754711i | \(0.727777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −225720. | −0.923060 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32076.0 | −0.126695 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −98307.0 | − | 170273.i | −0.362759 | − | 0.628318i | 0.625654 | − | 0.780100i | \(-0.284832\pi\) |
−0.988414 | + | 0.151782i | \(0.951499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37180.0 | + | 64397.6i | −0.132699 | + | 0.229841i | −0.924716 | − | 0.380658i | \(-0.875698\pi\) |
0.792017 | + | 0.610499i | \(0.209031\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −114912. | + | 199033.i | −0.384181 | + | 0.665421i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60439.0 | − | 104683.i | −0.195690 | − | 0.338945i | 0.751437 | − | 0.659805i | \(-0.229361\pi\) |
−0.947126 | + | 0.320861i | \(0.896028\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 361152. | 1.09806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −111340. | −0.328233 | −0.164116 | − | 0.986441i | \(-0.552477\pi\) | ||||
−0.164116 | + | 0.986441i | \(0.552477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 245916. | + | 425939.i | 0.682332 | + | 1.18183i | 0.974267 | + | 0.225395i | \(0.0723674\pi\) |
−0.291936 | + | 0.956438i | \(0.594299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 98284.5 | − | 170234.i | 0.264709 | − | 0.458489i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −353727. | + | 612673.i | −0.898572 | + | 1.55637i | −0.0692518 | + | 0.997599i | \(0.522061\pi\) |
−0.829320 | + | 0.558773i | \(0.811272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9196.00 | − | 15927.9i | −0.0226988 | − | 0.0393156i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 493668. | 1.15160 | 0.575801 | − | 0.817590i | \(-0.304690\pi\) | ||||
0.575801 | + | 0.817590i | \(0.304690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −559450. | −1.26930 | −0.634651 | − | 0.772799i | \(-0.718856\pi\) | ||||
−0.634651 | + | 0.772799i | \(0.718856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8046.00 | + | 13936.1i | 0.0172843 | + | 0.0299372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −160380. | + | 277786.i | −0.335387 | + | 0.580907i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 362016. | − | 627030.i | 0.718033 | − | 1.24367i | −0.243745 | − | 0.969839i | \(-0.578376\pi\) |
0.961778 | − | 0.273830i | \(-0.0882906\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3553.00 | − | 6153.98i | −0.00686597 | − | 0.0118922i | 0.862572 | − | 0.505934i | \(-0.168852\pi\) |
−0.869438 | + | 0.494042i | \(0.835519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −530442. | −0.973806 | −0.486903 | − | 0.873456i | \(-0.661873\pi\) | ||||
−0.486903 | + | 0.873456i | \(0.661873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 56168.0 | 0.100544 | 0.0502720 | − | 0.998736i | \(-0.483991\pi\) | ||||
0.0502720 | + | 0.998736i | \(0.483991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26136.0 | − | 45268.9i | −0.0445142 | − | 0.0771009i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −465102. | + | 805580.i | −0.772972 | + | 1.33883i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −225720. | + | 390959.i | −0.357441 | + | 0.619106i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 169598. | + | 293752.i | 0.262249 | + | 0.454229i | 0.966839 | − | 0.255385i | \(-0.0822023\pi\) |
−0.704590 | + | 0.709615i | \(0.748869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −653400. | −0.964013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −374528. | −0.539927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 124146. | + | 215027.i | 0.170983 | + | 0.296151i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −389680. | + | 674946.i | −0.524742 | + | 0.908880i | 0.474843 | + | 0.880071i | \(0.342505\pi\) |
−0.999585 | + | 0.0288094i | \(0.990828\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 372438. | − | 645082.i | 0.479722 | − | 0.830902i | −0.520008 | − | 0.854162i | \(-0.674071\pi\) |
0.999729 | + | 0.0232592i | \(0.00740430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 136373. | + | 236205.i | 0.171846 | + | 0.297646i | 0.939065 | − | 0.343739i | \(-0.111693\pi\) |
−0.767219 | + | 0.641385i | \(0.778360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −153846. | −0.185651 | −0.0928253 | − | 0.995682i | \(-0.529590\pi\) | ||||
−0.0928253 | + | 0.995682i | \(0.529590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69984.0 | −0.0826664 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −577368. | − | 1.00003e6i | −0.653820 | − | 1.13245i | −0.982188 | − | 0.187899i | \(-0.939832\pi\) |
0.328369 | − | 0.944550i | \(-0.393501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −328537. | + | 569043.i | −0.364369 | + | 0.631106i | −0.988675 | − | 0.150074i | \(-0.952049\pi\) |
0.624306 | + | 0.781180i | \(0.285382\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 244701. | − | 423835.i | 0.260448 | − | 0.451109i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 174724. | + | 302631.i | 0.182226 | + | 0.315625i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.34190e6 | 1.34442 | 0.672211 | − | 0.740359i | \(-0.265345\pi\) | ||||
0.672211 | + | 0.740359i | \(0.265345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.21616e6 | −2.17671 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −66177.0 | − | 114622.i | −0.0624992 | − | 0.108252i | 0.833083 | − | 0.553148i | \(-0.186574\pi\) |
−0.895582 | + | 0.444897i | \(0.853240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13112.0 | + | 22710.7i | −0.0121456 | + | 0.0210368i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −471636. | + | 816898.i | −0.420453 | + | 0.728246i | −0.995984 | − | 0.0895341i | \(-0.971462\pi\) |
0.575531 | + | 0.817780i | \(0.304796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −526338. | − | 911644.i | −0.460416 | − | 0.797463i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 967518. | 0.815227 | 0.407613 | − | 0.913155i | \(-0.366361\pi\) | ||||
0.407613 | + | 0.913155i | \(0.366361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −518320. | −0.428721 | −0.214360 | − | 0.976755i | \(-0.568767\pi\) | ||||
−0.214360 | + | 0.976755i | \(0.568767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 56430.0 | + | 97739.6i | 0.0449965 | + | 0.0779361i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.11136e6 | + | 1.92494e6i | −0.870275 | + | 1.50736i | −0.00856270 | + | 0.999963i | \(0.502726\pi\) |
−0.861712 | + | 0.507397i | \(0.830608\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 98307.0 | − | 170273.i | 0.0742709 | − | 0.128641i | −0.826498 | − | 0.562940i | \(-0.809670\pi\) |
0.900769 | + | 0.434299i | \(0.143004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 776138. | + | 1.34431e6i | 0.576067 | + | 0.997777i | 0.995925 | + | 0.0901872i | \(0.0287465\pi\) |
−0.419858 | + | 0.907590i | \(0.637920\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51589e6 | −1.08633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06702e6 | −0.751499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 536085. | + | 928526.i | 0.364808 | + | 0.631866i | 0.988745 | − | 0.149608i | \(-0.0478012\pi\) |
−0.623937 | + | 0.781475i | \(0.714468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 207036. | − | 358597.i | 0.138513 | − | 0.239912i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −857736. | + | 1.48564e6i | −0.554850 | + | 0.961029i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −532400. | − | 922144.i | −0.338705 | − | 0.586655i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.87585e6 | −1.15465 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.58589e6 | 0.960346 | 0.480173 | − | 0.877174i | \(-0.340574\pi\) | ||||
0.480173 | + | 0.877174i | \(0.340574\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 365364. | + | 632829.i | 0.214203 | + | 0.371010i | 0.953026 | − | 0.302890i | \(-0.0979514\pi\) |
−0.738823 | + | 0.673900i | \(0.764618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −292429. | + | 506502.i | −0.168717 | + | 0.292227i | −0.937969 | − | 0.346719i | \(-0.887296\pi\) |
0.769252 | + | 0.638946i | \(0.220629\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.24143e6 | − | 2.15023e6i | 0.693865 | − | 1.20181i | −0.276696 | − | 0.960957i | \(-0.589240\pi\) |
0.970562 | − | 0.240852i | \(-0.0774270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 160380. | + | 277786.i | 0.0882416 | + | 0.152839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 496584. | 0.264842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 87362.0 | 0.0458790 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −57024.0 | − | 98768.5i | −0.0290448 | − | 0.0503070i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −188974. | + | 327313.i | −0.0948052 | + | 0.164207i | −0.909527 | − | 0.415644i | \(-0.863556\pi\) |
0.814722 | + | 0.579852i | \(0.196889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −588924. | + | 1.02005e6i | −0.286713 | + | 0.496601i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −319561. | − | 553496.i | −0.153278 | − | 0.265485i | 0.779153 | − | 0.626834i | \(-0.215650\pi\) |
−0.932431 | + | 0.361349i | \(0.882316\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29824e6 | 1.07031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.27656e6 | 1.04483 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45233e6 | + | 2.51551e6i | 0.647503 | + | 1.12151i | 0.983717 | + | 0.179722i | \(0.0575199\pi\) |
−0.336215 | + | 0.941785i | \(0.609147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.99579e6 | − | 3.45680e6i | 0.877102 | − | 1.51919i | 0.0225958 | − | 0.999745i | \(-0.492807\pi\) |
0.854506 | − | 0.519441i | \(-0.173860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −714609. | + | 1.23774e6i | −0.305233 | + | 0.528679i | −0.977313 | − | 0.211799i | \(-0.932068\pi\) |
0.672080 | + | 0.740478i | \(0.265401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26554e6 | + | 2.19199e6i | 0.532974 | + | 0.923139i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.16186e6 | 0.475794 | 0.237897 | − | 0.971290i | \(-0.423542\pi\) | ||||
0.237897 | + | 0.971290i | \(0.423542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.77720e6 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.82417e6 | − | 3.15956e6i | −0.716695 | − | 1.24135i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 544616. | − | 943303.i | 0.211069 | − | 0.365583i | −0.740980 | − | 0.671527i | \(-0.765639\pi\) |
0.952049 | + | 0.305944i | \(0.0989721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 857736. | − | 1.48564e6i | 0.323533 | − | 0.560376i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.75288e6 | − | 3.03608e6i | −0.652350 | − | 1.12990i | −0.982551 | − | 0.185993i | \(-0.940450\pi\) |
0.330201 | − | 0.943911i | \(-0.392884\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 248292. | 0.0899724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.04385e6 | 1.44610 | 0.723048 | − | 0.690798i | \(-0.242740\pi\) | ||||
0.723048 | + | 0.690798i | \(0.242740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.59373e6 | − | 4.49247e6i | −0.903499 | − | 1.56491i | −0.822920 | − | 0.568157i | \(-0.807657\pi\) |
−0.0805786 | − | 0.996748i | \(-0.525677\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.28304e6 | − | 2.22229e6i | 0.441152 | − | 0.764098i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 475173. | − | 823024.i | 0.159213 | − | 0.275765i | −0.775372 | − | 0.631504i | \(-0.782438\pi\) |
0.934585 | + | 0.355740i | \(0.115771\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21889e6 | + | 2.11118e6i | 0.403201 | + | 0.698365i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.15325e6 | −1.33935 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −520738. | −0.165822 | −0.0829112 | − | 0.996557i | \(-0.526422\pi\) | ||||
−0.0829112 | + | 0.996557i | \(0.526422\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −382185. | − | 661964.i | −0.118690 | − | 0.205576i | 0.800559 | − | 0.599254i | \(-0.204536\pi\) |
−0.919249 | + | 0.393677i | \(0.871203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 889504. | − | 1.54067e6i | 0.272826 | − | 0.472548i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 80460.0 | − | 139361.i | 0.0240765 | − | 0.0417018i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.32025e6 | − | 2.28675e6i | −0.390255 | − | 0.675942i | 0.602228 | − | 0.798324i | \(-0.294280\pi\) |
−0.992483 | + | 0.122382i | \(0.960947\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 674784. | 0.194666 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.65666e6 | 1.04223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.49010e6 | + | 4.31298e6i | 0.692918 | + | 1.20017i | 0.970877 | + | 0.239577i | \(0.0770087\pi\) |
−0.277959 | + | 0.960593i | \(0.589658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 118997. | − | 206109.i | 0.0327213 | − | 0.0566750i | −0.849201 | − | 0.528070i | \(-0.822916\pi\) |
0.881922 | + | 0.471395i | \(0.156249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 62073.0 | − | 107514.i | 0.0166698 | − | 0.0288729i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.52847e6 | − | 2.64739e6i | −0.405684 | − | 0.702665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.88238e6 | −1.00671 | −0.503356 | − | 0.864079i | \(-0.667902\pi\) | ||||
−0.503356 | + | 0.864079i | \(0.667902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −66958.0 | −0.0171626 | −0.00858129 | − | 0.999963i | \(-0.502732\pi\) | ||||
−0.00858129 | + | 0.999963i | \(0.502732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.71547e6 | + | 2.97128e6i | 0.429715 | + | 0.744287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.25068e6 | − | 5.63034e6i | 0.805031 | − | 1.39435i | −0.111240 | − | 0.993794i | \(-0.535482\pi\) |
0.916270 | − | 0.400560i | \(-0.131184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.30380e6 | − | 3.99030e6i | 0.557745 | − | 0.966043i | −0.439939 | − | 0.898028i | \(-0.645000\pi\) |
0.997684 | − | 0.0680154i | \(-0.0216667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −803358. | − | 1.39146e6i | −0.192313 | − | 0.333096i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.77671e6 | 0.884092 | 0.442046 | − | 0.896992i | \(-0.354253\pi\) | ||||
0.442046 | + | 0.896992i | \(0.354253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.30204e6 | 2.15346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −993168. | − | 1.72022e6i | −0.224902 | − | 0.389543i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.59035e6 | − | 2.75456e6i | 0.356206 | − | 0.616967i | −0.631117 | − | 0.775687i | \(-0.717403\pi\) |
0.987324 | + | 0.158720i | \(0.0507368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.34274e6 | + | 5.78979e6i | −0.732571 | + | 1.26885i | 0.223210 | + | 0.974770i | \(0.428346\pi\) |
−0.955781 | + | 0.294080i | \(0.904987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.17561e6 | + | 3.76826e6i | 0.471659 | + | 0.816937i | 0.999474 | − | 0.0324218i | \(-0.0103220\pi\) |
−0.527815 | + | 0.849359i | \(0.676989\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.07994e6 | 1.50223 | 0.751117 | − | 0.660170i | \(-0.229516\pi\) | ||||
0.751117 | + | 0.660170i | \(0.229516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91946e6 | −0.402945 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.26700e6 | + | 5.65861e6i | 0.671423 | + | 1.16294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 87362.0 | − | 151315.i | 0.0177660 | − | 0.0307715i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.61093e6 | + | 2.79021e6i | −0.320802 | + | 0.555646i | −0.980654 | − | 0.195750i | \(-0.937286\pi\) |
0.659852 | + | 0.751396i | \(0.270619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −62282.0 | − | 107876.i | −0.0122744 | − | 0.0212599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.60949e6 | −1.27589 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29710e6 | 0.438891 | 0.219446 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219446 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.41075e6 | − | 2.44349e6i | −0.264087 | − | 0.457411i | 0.703237 | − | 0.710955i | \(-0.251737\pi\) |
−0.967324 | + | 0.253544i | \(0.918404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 176418. | − | 305565.i | 0.0326908 | − | 0.0566221i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.06237e6 | + | 3.57213e6i | −0.374520 | + | 0.648688i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.06814e6 | + | 3.58213e6i | 0.371817 | + | 0.644006i | 0.989845 | − | 0.142150i | \(-0.0454016\pi\) |
−0.618028 | + | 0.786156i | \(0.712068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.33263e6 | 1.46846 | 0.734230 | − | 0.678901i | \(-0.237543\pi\) | ||||
0.734230 | + | 0.678901i | \(0.237543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 609444. | 0.106342 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.17050e6 | − | 3.75942e6i | −0.371335 | − | 0.643171i | 0.618436 | − | 0.785835i | \(-0.287767\pi\) |
−0.989771 | + | 0.142664i | \(0.954433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.97273e6 | − | 5.14892e6i | 0.503620 | − | 0.872295i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 735912. | − | 1.27464e6i | 0.122267 | − | 0.211772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 349920. | + | 606079.i | 0.0575761 | + | 0.0997248i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.74185e6 | −1.08814 | −0.544070 | − | 0.839040i | \(-0.683117\pi\) | ||||
−0.544070 | + | 0.839040i | \(0.683117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.72196e6 | −1.23445 | −0.617224 | − | 0.786787i | \(-0.711743\pi\) | ||||
−0.617224 | + | 0.786787i | \(0.711743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.26403e6 | − | 2.18937e6i | −0.198258 | − | 0.343394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.20324e6 | + | 9.01227e6i | −0.808415 | + | 1.40022i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.60023e6 | − | 6.23579e6i | 0.548925 | − | 0.950765i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.30383e6 | − | 5.72240e6i | −0.499037 | − | 0.864358i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.89402e6 | −0.725594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −682066. | −0.100192 | −0.0500960 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500960 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.69735e6 | − | 4.67195e6i | −0.388997 | − | 0.673763i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.07886e6 | + | 1.86864e6i | −0.154169 | + | 0.267028i | −0.932756 | − | 0.360508i | \(-0.882603\pi\) |
0.778587 | + | 0.627536i | \(0.215937\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 248292. | − | 430054.i | 0.0348404 | − | 0.0603454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.38413e6 | − | 5.86148e6i | −0.470581 | − | 0.815069i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.67597e6 | −0.365463 | −0.182731 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182731 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.05780e6 | 0.684592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.77665e6 | + | 3.07725e6i | 0.236228 | + | 0.409159i | 0.959629 | − | 0.281269i | \(-0.0907554\pi\) |
−0.723401 | + | 0.690428i | \(0.757422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 800442. | − | 1.38641e6i | 0.105489 | − | 0.182713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.46123e6 | − | 1.11912e7i | 0.836633 | − | 1.44909i | −0.0560613 | − | 0.998427i | \(-0.517854\pi\) |
0.892694 | − | 0.450663i | \(-0.148812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.04179e6 | + | 5.26853e6i | 0.390426 | + | 0.676237i | 0.992506 | − | 0.122199i | \(-0.0389945\pi\) |
−0.602080 | + | 0.798436i | \(0.705661\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 857736. | 0.108189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.58241e7 | −1.97869 | −0.989347 | − | 0.145579i | \(-0.953495\pi\) | ||||
−0.989347 | + | 0.145579i | \(0.953495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.97950e6 | + | 5.16065e6i | 0.366188 | + | 0.634256i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.26338e6 | + | 9.11644e6i | −0.641347 | + | 1.11085i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.30110e6 | + | 3.98563e6i | −0.275639 | + | 0.477421i | −0.970296 | − | 0.241920i | \(-0.922223\pi\) |
0.694657 | + | 0.719341i | \(0.255556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.77901e6 | − | 3.08133e6i | −0.211295 | − | 0.365974i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.61122e6 | 1.00561 | 0.502803 | − | 0.864401i | \(-0.332302\pi\) | ||||
0.502803 | + | 0.864401i | \(0.332302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.82269e6 | −0.326867 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.99114e6 | + | 6.91286e6i | 0.454496 | + | 0.787210i | 0.998659 | − | 0.0517695i | \(-0.0164861\pi\) |
−0.544163 | + | 0.838979i | \(0.683153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.08700e6 | + | 8.81095e6i | −0.574481 | + | 0.995031i | 0.421616 | + | 0.906774i | \(0.361463\pi\) |
−0.996098 | + | 0.0882567i | \(0.971870\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.52482e6 | + | 6.10517e6i | −0.391515 | + | 0.678125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.97922e6 | + | 8.62426e6i | 0.548516 | + | 0.950057i | 0.998377 | + | 0.0569587i | \(0.0181403\pi\) |
−0.449861 | + | 0.893099i | \(0.648526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 541728. | 0.0587054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.19586e6 | 0.450993 | 0.225497 | − | 0.974244i | \(-0.427600\pi\) | ||||
0.225497 | + | 0.974244i | \(0.427600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.56276e6 | − | 7.90293e6i | −0.482519 | − | 0.835747i | 0.517280 | − | 0.855816i | \(-0.326945\pi\) |
−0.999799 | + | 0.0200690i | \(0.993611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.22867e6 | + | 5.59222e6i | −0.338686 | + | 0.586621i | −0.984186 | − | 0.177139i | \(-0.943316\pi\) |
0.645500 | + | 0.763760i | \(0.276649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.30918e6 | − | 2.26756e6i | 0.135138 | − | 0.234066i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.53441e6 | + | 7.85383e6i | 0.464324 | + | 0.804232i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −177012. | −0.0178392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.40514e7 | −1.40490 | −0.702450 | − | 0.711733i | \(-0.747910\pi\) | ||||
−0.702450 | + | 0.711733i | \(0.747910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.08582e6 | − | 1.57371e7i | −0.894190 | − | 1.54878i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.89417e6 | + | 3.28079e6i | −0.184957 | + | 0.320354i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.23584e6 | + | 7.33669e6i | −0.407188 | + | 0.705270i | −0.994573 | − | 0.104037i | \(-0.966824\pi\) |
0.587386 | + | 0.809307i | \(0.300157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −244282. | − | 423109.i | −0.0233004 | − | 0.0403575i | 0.854140 | − | 0.520043i | \(-0.174084\pi\) |
−0.877441 | + | 0.479685i | \(0.840751\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.48119e6 | 0.233023 | 0.116512 | − | 0.993189i | \(-0.462829\pi\) | ||||
0.116512 | + | 0.993189i | \(0.462829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.14072e6 | −0.385891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.64565e6 | + | 4.58240e6i | 0.242800 | + | 0.420543i | 0.961511 | − | 0.274767i | \(-0.0886007\pi\) |
−0.718711 | + | 0.695309i | \(0.755267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.72646e6 | + | 4.72237e6i | −0.248311 | + | 0.430087i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.36234e6 | + | 4.09169e6i | −0.211899 | + | 0.367019i | −0.952309 | − | 0.305136i | \(-0.901298\pi\) |
0.740410 | + | 0.672156i | \(0.234631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.08710e6 | + | 5.34702e6i | 0.274819 | + | 0.476001i | 0.970090 | − | 0.242747i | \(-0.0780486\pi\) |
−0.695270 | + | 0.718748i | \(0.744715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.97267e6 | −0.348360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.43778e6 | 0.212168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.37926e6 | + | 1.62454e7i | 0.804197 | + | 1.39291i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.70462e6 | − | 8.14865e6i | 0.400394 | − | 0.693502i | −0.593380 | − | 0.804923i | \(-0.702207\pi\) |
0.993773 | + | 0.111421i | \(0.0355401\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.50430e6 | + | 1.29978e7i | −0.629272 | + | 1.08993i | 0.358426 | + | 0.933558i | \(0.383314\pi\) |
−0.987698 | + | 0.156373i | \(0.950020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.38551e6 | − | 9.32798e6i | −0.448283 | − | 0.776449i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.29707e7 | −1.06393 | −0.531963 | − | 0.846768i | \(-0.678545\pi\) | ||||
−0.531963 | + | 0.846768i | \(0.678545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.71257e7 | −1.39451 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.07425e6 | + | 7.05680e6i | 0.326963 | + | 0.566317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.13278e7 | + | 1.96203e7i | −0.902506 | + | 1.56319i | −0.0782761 | + | 0.996932i | \(0.524942\pi\) |
−0.824230 | + | 0.566255i | \(0.808392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00475e6 | − | 6.93643e6i | 0.314495 | − | 0.544721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.11612e6 | − | 8.86138e6i | −0.398895 | − | 0.690907i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.90169e7 | 1.46166 | 0.730828 | − | 0.682562i | \(-0.239134\pi\) | ||||
0.730828 | + | 0.682562i | \(0.239134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −249128. | −0.0190123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 496584. | + | 860109.i | 0.0373632 | + | 0.0647150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.56556e6 | + | 1.31039e7i | −0.565231 | + | 0.979008i | 0.431798 | + | 0.901971i | \(0.357879\pi\) |
−0.997028 | + | 0.0770376i | \(0.975454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.73331e6 | − | 1.51265e7i | 0.643362 | − | 1.11434i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.09444e6 | + | 1.05559e7i | 0.445829 | + | 0.772199i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50323e7 | −1.08443 | −0.542217 | − | 0.840238i | \(-0.682415\pi\) | ||||
−0.542217 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39853e6 | 0.171833 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −62073.0 | − | 107514.i | −0.00438589 | − | 0.00759658i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.70615e6 | − | 6.41924e6i | 0.260068 | − | 0.450451i | −0.706192 | − | 0.708021i | \(-0.749588\pi\) |
0.966260 | + | 0.257570i | \(0.0829217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.59370e6 | − | 6.22447e6i | 0.248742 | − | 0.430833i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38964e6 | + | 2.40693e6i | 0.0955306 | + | 0.165464i | 0.909830 | − | 0.414981i | \(-0.136212\pi\) |
−0.814299 | + | 0.580445i | \(0.802879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17785e7 | 0.798768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.21046e7 | −0.815342 | −0.407671 | − | 0.913129i | \(-0.633659\pi\) | ||||
−0.407671 | + | 0.913129i | \(0.633659\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.23463e6 | − | 3.87049e6i | −0.148502 | − | 0.257214i | 0.782172 | − | 0.623063i | \(-0.214112\pi\) |
−0.930674 | + | 0.365849i | \(0.880779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.30858e6 | + | 9.19473e6i | −0.350419 | + | 0.606943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.38402e6 | − | 9.32539e6i | 0.350673 | − | 0.607383i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.44231e7 | − | 2.49816e7i | −0.933168 | − | 1.61629i | −0.777869 | − | 0.628426i | \(-0.783700\pi\) |
−0.155298 | − | 0.987868i | \(-0.549634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.01544e6 | 0.256369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.60868e6 | 0.609430 | 0.304715 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304715 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.27294e6 | − | 3.93685e6i | −0.142274 | − | 0.246426i | 0.786078 | − | 0.618127i | \(-0.212108\pi\) |
−0.928353 | + | 0.371700i | \(0.878775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.39569e6 | − | 7.61355e6i | 0.273348 | − | 0.473452i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.60261e6 | + | 2.77581e6i | −0.0983649 | + | 0.170373i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.07962e7 | + | 1.86995e7i | 0.658345 | + | 1.14029i | 0.981044 | + | 0.193785i | \(0.0620765\pi\) |
−0.322699 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.48400e7 | −0.893276 | −0.446638 | − | 0.894715i | \(-0.647379\pi\) | ||||
−0.446638 | + | 0.894715i | \(0.647379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −889504. | −0.0531978 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.20047e6 | − | 1.24716e7i | −0.425125 | − | 0.736339i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.26554e7 | − | 2.19199e7i | 0.742420 | − | 1.28591i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26371e6 | + | 5.65290e6i | −0.189033 | + | 0.327414i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.24393e7 | + | 2.15454e7i | 0.715909 | + | 1.23999i | 0.962608 | + | 0.270898i | \(0.0873208\pi\) |
−0.246699 | + | 0.969092i | \(0.579346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.60885e6 | 0.148254 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.45205e7 | 0.819970 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.58040e7 | − | 2.73733e7i | −0.881294 | − | 1.52645i | −0.849903 | − | 0.526939i | \(-0.823339\pi\) |
−0.0313914 | − | 0.999507i | \(-0.509994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 384912. | − | 666687.i | 0.0213302 | − | 0.0369450i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.82417e7 | + | 3.15956e7i | −0.998338 | + | 1.72917i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.75110e6 | − | 1.68894e7i | −0.530352 | − | 0.918596i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.10009e6 | −0.166534 | −0.0832669 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832669 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87180e6 | 0.0999328 | 0.0499664 | − | 0.998751i | \(-0.484089\pi\) | ||||
0.0499664 | + | 0.998751i | \(0.484089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00618e6 | + | 5.20686e6i | 0.158533 | + | 0.274588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.05780e6 | − | 8.76037e6i | 0.265098 | − | 0.459163i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00092e7 | − | 1.73364e7i | 0.518252 | − | 0.897640i | −0.481523 | − | 0.876434i | \(-0.659916\pi\) |
0.999775 | − | 0.0212059i | \(-0.00675056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.65588e6 | − | 1.32604e7i | −0.394000 | − | 0.682427i | 0.598973 | − | 0.800769i | \(-0.295576\pi\) |
−0.992973 | + | 0.118342i | \(0.962242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.59310e6 | 0.487748 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.52209e7 | 1.27460 | 0.637302 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637302 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.69171e6 | + | 4.66218e6i | 0.134405 | + | 0.232797i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.32795e7 | − | 2.30007e7i | 0.659120 | − | 1.14163i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.88116e6 | − | 1.53826e7i | 0.435577 | − | 0.754442i | −0.561765 | − | 0.827297i | \(-0.689878\pi\) |
0.997343 | + | 0.0728549i | \(0.0232110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00792e7 | + | 1.74576e7i | 0.491399 | + | 0.851128i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.06147e7 | −0.511407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.14883e7 | −0.550234 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −611496. | − | 1.05914e6i | −0.0289447 | − | 0.0501338i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 243485. | − | 421728.i | 0.0114578 | − | 0.0198454i | −0.860240 | − | 0.509890i | \(-0.829686\pi\) |
0.871697 | + | 0.490044i | \(0.163019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 963171. | − | 1.66826e6i | 0.0447972 | − | 0.0775911i | −0.842757 | − | 0.538294i | \(-0.819069\pi\) |
0.887555 | + | 0.460702i | \(0.152402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.11769e7 | − | 1.93590e7i | −0.516820 | − | 0.895158i | −0.999809 | − | 0.0195320i | \(-0.993782\pi\) |
0.482989 | − | 0.875626i | \(-0.339551\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.85838e7 | 0.849390 | 0.424695 | − | 0.905337i | \(-0.360381\pi\) | ||||
0.424695 | + | 0.905337i | \(0.360381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.82025e7 | 1.73601 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.07662e7 | + | 3.59682e7i | 0.932843 | + | 1.61573i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.55871e6 | − | 7.89591e6i | 0.203609 | − | 0.352661i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.92158e6 | + | 1.37206e7i | −0.349778 | + | 0.605832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.45524e7 | + | 2.52055e7i | 0.638905 | + | 1.10662i | 0.985673 | + | 0.168665i | \(0.0539456\pi\) |
−0.346769 | + | 0.937951i | \(0.612721\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.14696e6 | −0.136600 | −0.0683001 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683001 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.59995e7 | 0.690566 | 0.345283 | − | 0.938499i | \(-0.387783\pi\) | ||||
0.345283 | + | 0.938499i | \(0.387783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.72937e7 | + | 2.99536e7i | 0.738039 | + | 1.27832i | 0.953377 | + | 0.301781i | \(0.0975813\pi\) |
−0.215338 | + | 0.976540i | \(0.569085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.48065e7 | − | 2.56457e7i | 0.628346 | − | 1.08833i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 541728. | − | 938300.i | 0.0227328 | − | 0.0393743i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.33290e7 | − | 2.30866e7i | −0.556213 | − | 0.963389i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.52806e6 | −0.104325 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.15794e7 | 0.475199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.51052e7 | + | 2.61629e7i | 0.613061 | + | 1.06185i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.71982e6 | + | 1.51032e7i | −0.351957 | + | 0.609607i | −0.986592 | − | 0.163205i | \(-0.947817\pi\) |
0.634635 | + | 0.772812i | \(0.281150\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.29794e6 | − | 2.24810e6i | 0.0518155 | − | 0.0897471i | −0.838954 | − | 0.544202i | \(-0.816833\pi\) |
0.890770 | + | 0.454455i | \(0.150166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.82833e7 | − | 3.16676e7i | −0.725902 | − | 1.25730i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.88624e6 | −0.348975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.76411e7 | −0.689028 | −0.344514 | − | 0.938781i | \(-0.611956\pi\) | ||||
−0.344514 | + | 0.938781i | \(0.611956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.79625e6 | − | 1.69676e7i | −0.378491 | − | 0.655566i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31141.0 | + | 53937.8i | −0.00119668 | + | 0.00207271i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.98392e7 | + | 3.43626e7i | −0.754199 | + | 1.30631i | 0.191573 | + | 0.981478i | \(0.438641\pi\) |
−0.945772 | + | 0.324833i | \(0.894692\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.78833e6 | + | 6.56159e6i | 0.143243 | + | 0.248105i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.73210e7 | 0.647955 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.93413e7 | 1.46386 | 0.731930 | − | 0.681380i | \(-0.238620\pi\) | ||||
0.731930 | + | 0.681380i | \(0.238620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.31253e7 | − | 4.00542e7i | −0.851361 | − | 1.47460i | −0.879981 | − | 0.475009i | \(-0.842445\pi\) |
0.0286202 | − | 0.999590i | \(-0.490889\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.53478e7 | − | 6.12241e7i | 1.29444 | − | 2.24204i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.89512e7 | − | 3.28245e7i | 0.686693 | − | 1.18939i | −0.286208 | − | 0.958167i | \(-0.592395\pi\) |
0.972901 | − | 0.231220i | \(-0.0742718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.41205e7 | + | 2.44574e7i | 0.508960 | + | 0.881544i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.66462e7 | −0.950394 | −0.475197 | − | 0.879879i | \(-0.657623\pi\) | ||||
−0.475197 | + | 0.879879i | \(0.657623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.90977e7 | −1.38721 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.39542e7 | − | 2.41695e7i | −0.489959 | − | 0.848634i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.25781e6 | − | 9.10679e6i | 0.183652 | − | 0.318095i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −191862. | + | 332315.i | −0.00663240 | + | 0.0114877i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.04895e7 | − | 3.54889e7i | −0.704637 | − | 1.22047i | −0.966822 | − | 0.255450i | \(-0.917776\pi\) |
0.262185 | − | 0.965018i | \(-0.415557\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.72034e7 | −0.925922 | −0.462961 | − | 0.886379i | \(-0.653213\pi\) | ||||
−0.462961 | + | 0.886379i | \(0.653213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.30525e7 | 0.441990 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.26778e7 | − | 2.19585e7i | −0.424919 | − | 0.735982i | 0.571494 | − | 0.820607i | \(-0.306364\pi\) |
−0.996413 | + | 0.0846247i | \(0.973031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.03358e6 | + | 1.39146e7i | −0.267887 | + | 0.463995i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.95696e6 | + | 1.03178e7i | −0.196626 | + | 0.340566i | −0.947432 | − | 0.319956i | \(-0.896332\pi\) |
0.750806 | + | 0.660522i | \(0.229665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.43219e7 | + | 2.48063e7i | 0.470339 | + | 0.814651i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.96584e7 | 1.61437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91931e7 | 0.944268 | 0.472134 | − | 0.881527i | \(-0.343484\pi\) | ||||
0.472134 | + | 0.881527i | \(0.343484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.51654e6 | − | 2.62672e6i | −0.0485618 | − | 0.0841116i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.65004e6 | − | 1.49823e7i | 0.275601 | − | 0.477354i | −0.694686 | − | 0.719313i | \(-0.744457\pi\) |
0.970286 | + | 0.241959i | \(0.0777900\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))