Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(385,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.385");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.d (of order \(2\), degree \(1\), 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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 385.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.385 |
Dual form | 768.4.d.j.385.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.0000i | 1.60997i | 0.593296 | + | 0.804984i | \(0.297826\pi\) | ||||
−0.593296 | + | 0.804984i | \(0.702174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000i | 0.986764i | 0.869813 | + | 0.493382i | \(0.164240\pi\) | ||||
−0.869813 | + | 0.493382i | \(0.835760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 10.0000i | − 0.213346i | −0.994294 | − | 0.106673i | \(-0.965980\pi\) | ||||
0.994294 | − | 0.106673i | \(-0.0340198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000 | 0.929516 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459015\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.000i | 1.20745i | 0.797192 | + | 0.603726i | \(0.206318\pi\) | ||||
−0.797192 | + | 0.603726i | \(0.793682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 24.0000i | − 0.249392i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −199.000 | −1.59200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 234.000i | − 1.49837i | −0.662361 | − | 0.749185i | \(-0.730446\pi\) | ||||
0.662361 | − | 0.749185i | \(-0.269554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.0000 | 0.0926995 | 0.0463498 | − | 0.998925i | \(-0.485241\pi\) | ||||
0.0463498 | + | 0.998925i | \(0.485241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 108.000 | 0.569709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 144.000i | 0.695441i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 226.000i | 1.00417i | 0.864819 | + | 0.502083i | \(0.167433\pi\) | ||||
−0.864819 | + | 0.502083i | \(0.832567\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −30.0000 | −0.123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −90.0000 | −0.342820 | −0.171410 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171410 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 452.000i | 1.60301i | 0.597989 | + | 0.801504i | \(0.295967\pi\) | ||||
−0.597989 | + | 0.801504i | \(0.704033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 162.000i | − 0.536656i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −432.000 | −1.34072 | −0.670358 | − | 0.742038i | \(-0.733860\pi\) | ||||
−0.670358 | + | 0.742038i | \(0.733860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 54.0000i | − 0.148265i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 414.000i | − 1.07297i | −0.843911 | − | 0.536484i | \(-0.819752\pi\) | ||||
0.843911 | − | 0.536484i | \(-0.180248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −648.000 | −1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 300.000 | 0.697122 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 684.000i | − 1.50931i | −0.656123 | − | 0.754654i | \(-0.727805\pi\) | ||||
0.656123 | − | 0.754654i | \(-0.272195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 422.000i | 0.885763i | 0.896580 | + | 0.442882i | \(0.146044\pi\) | ||||
−0.896580 | + | 0.442882i | \(0.853956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72.0000 | −0.143986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 180.000 | 0.343481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 332.000i | − 0.605377i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) | ||||
0.953090 | − | 0.302688i | \(-0.0978842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 216.000i | − 0.376860i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −360.000 | −0.601748 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26.0000 | −0.0416859 | −0.0208429 | − | 0.999783i | \(-0.506635\pi\) | ||||
−0.0208429 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 597.000i | 0.919142i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 288.000i | 0.426242i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −512.000 | −0.729171 | −0.364585 | − | 0.931170i | \(-0.618789\pi\) | ||||
−0.364585 | + | 0.931170i | \(0.618789\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1188.00i | 1.57108i | 0.618809 | + | 0.785542i | \(0.287616\pi\) | ||||
−0.618809 | + | 0.785542i | \(0.712384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 324.000i | 0.413444i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −702.000 | −0.865084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 630.000 | 0.750336 | 0.375168 | − | 0.926957i | \(-0.377585\pi\) | ||||
0.375168 | + | 0.926957i | \(0.377585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 80.0000i | − 0.0921569i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 48.0000i | − 0.0535201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1800.00 | −1.94396 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1054.00 | −1.10327 | −0.551637 | − | 0.834085i | \(-0.685996\pi\) | ||||
−0.551637 | + | 0.834085i | \(0.685996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 324.000i | − 0.328921i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 558.000i | − 0.549733i | −0.961482 | − | 0.274867i | \(-0.911366\pi\) | ||||
0.961482 | − | 0.274867i | \(-0.0886337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.00765304 | 0.00382652 | − | 0.999993i | \(-0.498782\pi\) | ||||
0.00382652 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 432.000 | 0.401513 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1764.00i | 1.59376i | 0.604138 | + | 0.796880i | \(0.293518\pi\) | ||||
−0.604138 | + | 0.796880i | \(0.706482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1622.00i | 1.42532i | 0.701512 | + | 0.712658i | \(0.252509\pi\) | ||||
−0.701512 | + | 0.712658i | \(0.747491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 678.000 | 0.579756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1134.00 | −0.944051 | −0.472025 | − | 0.881585i | \(-0.656477\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1296.00i | 1.05089i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 90.0000i | 0.0711154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 144.000 | 0.110928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 35.0000 | 0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 270.000i | 0.197927i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1332.00i | − 0.953102i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 592.000 | 0.413634 | 0.206817 | − | 0.978380i | \(-0.433690\pi\) | ||||
0.206817 | + | 0.978380i | \(0.433690\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1356.00 | 0.925497 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1908.00i | 1.27254i | 0.771466 | + | 0.636270i | \(0.219524\pi\) | ||||
−0.771466 | + | 0.636270i | \(0.780476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 800.000i | 0.521570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −486.000 | −0.309839 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −954.000 | −0.594932 | −0.297466 | − | 0.954732i | \(-0.596142\pi\) | ||||
−0.297466 | + | 0.954732i | \(0.596142\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2564.00i | 1.56457i | 0.622919 | + | 0.782286i | \(0.285947\pi\) | ||||
−0.622919 | + | 0.782286i | \(0.714053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1296.00i | 0.774063i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 360.000 | 0.210522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4212.00 | 2.41233 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 837.000i | 0.469623i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 738.000i | 0.405767i | 0.979203 | + | 0.202884i | \(0.0650313\pi\) | ||||
−0.979203 | + | 0.202884i | \(0.934969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2440.00 | −1.31500 | −0.657498 | − | 0.753456i | \(-0.728385\pi\) | ||||
−0.657498 | + | 0.753456i | \(0.728385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −162.000 | −0.0856008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 288.000i | 0.149243i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2554.00i | − 1.29829i | −0.760665 | − | 0.649145i | \(-0.775127\pi\) | ||||
0.760665 | − | 0.649145i | \(-0.224873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1242.00 | −0.619478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 576.000 | 0.281958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 820.000i | 0.394033i | 0.980400 | + | 0.197016i | \(0.0631252\pi\) | ||||
−0.980400 | + | 0.197016i | \(0.936875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1944.00i | 0.917213i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1944.00 | 0.900786 | 0.450393 | − | 0.892830i | \(-0.351284\pi\) | ||||
0.450393 | + | 0.892830i | \(0.351284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2097.00 | 0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 900.000i | − 0.402484i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1242.00i | − 0.545824i | −0.962039 | − | 0.272912i | \(-0.912013\pi\) | ||||
0.962039 | − | 0.272912i | \(-0.0879867\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1592.00 | −0.687679 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2052.00 | −0.871400 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1116.00i | − 0.465999i | −0.972477 | − | 0.232999i | \(-0.925146\pi\) | ||||
0.972477 | − | 0.232999i | \(-0.0748540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1070.00i | − 0.439406i | −0.975567 | − | 0.219703i | \(-0.929491\pi\) | ||||
0.975567 | − | 0.219703i | \(-0.0705088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1266.00 | 0.511396 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4068.00 | −1.61668 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 648.000i | 0.253403i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 216.000i | 0.0831306i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 576.000 | 0.218209 | 0.109104 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1342.00 | −0.500514 | −0.250257 | − | 0.968179i | \(-0.580515\pi\) | ||||
−0.250257 | + | 0.968179i | \(0.580515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 540.000i | − 0.198309i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1422.00i | − 0.514281i | −0.966374 | − | 0.257140i | \(-0.917220\pi\) | ||||
0.966374 | − | 0.257140i | \(-0.0827803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 872.000 | 0.310625 | 0.155313 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155313 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −996.000 | −0.349515 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1872.00i | − 0.647235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1620.00i | − 0.551930i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3600.00 | −1.19147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1340.00i | − 0.437201i | −0.975814 | − | 0.218600i | \(-0.929851\pi\) | ||||
0.975814 | − | 0.218600i | \(-0.0701491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1080.00i | 0.347420i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8136.00 | −2.58079 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 128.000 | 0.0400424 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 78.0000i | 0.0240674i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 180.000i | − 0.0547878i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4880.00 | −1.46542 | −0.732711 | − | 0.680540i | \(-0.761745\pi\) | ||||
−0.732711 | + | 0.680540i | \(0.761745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2700.00i | − 0.789451i | −0.918799 | − | 0.394725i | \(-0.870840\pi\) | ||||
0.918799 | − | 0.394725i | \(-0.129160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 254.000i | − 0.0732960i | −0.999328 | − | 0.0366480i | \(-0.988332\pi\) | ||||
0.999328 | − | 0.0366480i | \(-0.0116680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 864.000 | 0.246091 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4410.00 | −1.23995 | −0.619976 | − | 0.784621i | \(-0.712858\pi\) | ||||
−0.619976 | + | 0.784621i | \(0.712858\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7776.00i | − 2.15851i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1536.00i | 0.420987i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3888.00 | 1.05228 | 0.526138 | − | 0.850399i | \(-0.323640\pi\) | ||||
0.526138 | + | 0.850399i | \(0.323640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5138.00 | 1.37331 | 0.686655 | − | 0.726984i | \(-0.259078\pi\) | ||||
0.686655 | + | 0.726984i | \(0.259078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 5022.00i | − 1.30957i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1000.00 | 0.257605 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3564.00 | 0.907066 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4788.00i | 1.20405i | 0.798478 | + | 0.602024i | \(0.205639\pi\) | ||||
−0.798478 | + | 0.602024i | \(0.794361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2592.00i | 0.644101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 972.000 | 0.238702 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5886.00 | −1.42863 | −0.714316 | − | 0.699823i | \(-0.753262\pi\) | ||||
−0.714316 | + | 0.699823i | \(0.753262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1808.00i | 0.433759i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2106.00i | 0.499456i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2232.00 | 0.523312 | 0.261656 | − | 0.965161i | \(-0.415731\pi\) | ||||
0.261656 | + | 0.965161i | \(0.415731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7452.00 | 1.72744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1890.00i | − 0.433206i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 666.000i | − 0.150954i | −0.997148 | − | 0.0754772i | \(-0.975952\pi\) | ||||
0.997148 | − | 0.0754772i | \(-0.0240480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5536.00 | 1.24092 | 0.620458 | − | 0.784240i | \(-0.286947\pi\) | ||||
0.620458 | + | 0.784240i | \(0.286947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −240.000 | −0.0532068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7164.00i | − 1.57093i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2126.00i | − 0.461151i | −0.973054 | − | 0.230576i | \(-0.925939\pi\) | ||||
0.973054 | − | 0.230576i | \(-0.0740609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −144.000 | −0.0308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2934.00 | 0.622875 | 0.311437 | − | 0.950267i | \(-0.399190\pi\) | ||||
0.311437 | + | 0.950267i | \(0.399190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2036.00i | 0.427659i | 0.976871 | + | 0.213830i | \(0.0685938\pi\) | ||||
−0.976871 | + | 0.213830i | \(0.931406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5400.00i | 1.12235i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −720.000 | −0.148085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3162.00i | 0.636975i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2286.00i | − 0.455800i | −0.973684 | − | 0.227900i | \(-0.926814\pi\) | ||||
0.973684 | − | 0.227900i | \(-0.0731860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12312.0 | 2.42994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −972.000 | −0.189903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 720.000i | − 0.139260i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3616.00i | 0.692434i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1674.00 | −0.317389 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7596.00 | −1.42605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1244.00i | − 0.231267i | −0.993292 | − | 0.115633i | \(-0.963110\pi\) | ||||
0.993292 | − | 0.115633i | \(-0.0368897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 24.0000i | − 0.00441849i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1224.00 | 0.223173 | 0.111586 | − | 0.993755i | \(-0.464407\pi\) | ||||
0.111586 | + | 0.993755i | \(0.464407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1898.00 | −0.342752 | −0.171376 | − | 0.985206i | \(-0.554821\pi\) | ||||
−0.171376 | + | 0.985206i | \(0.554821\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1296.00i | − 0.231814i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9162.00i | − 1.62331i | −0.584137 | − | 0.811655i | \(-0.698567\pi\) | ||||
0.584137 | − | 0.811655i | \(-0.301433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8424.00 | 1.47854 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5292.00 | 0.920158 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1800.00i | 0.310076i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1990.00i | 0.339647i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4866.00 | 0.822906 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3456.00 | −0.579135 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4348.00i | − 0.722017i | −0.932562 | − | 0.361009i | \(-0.882432\pi\) | ||||
0.932562 | − | 0.361009i | \(-0.117568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2034.00i | − 0.334722i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5976.00 | 0.974638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7154.00 | 1.15639 | 0.578195 | − | 0.815899i | \(-0.303757\pi\) | ||||
0.578195 | + | 0.815899i | \(0.303757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3402.00i | 0.545048i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 576.000i | 0.0914726i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3888.00 | 0.606733 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1836.00i | − 0.284039i | −0.989864 | − | 0.142020i | \(-0.954640\pi\) | ||||
0.989864 | − | 0.142020i | \(-0.0453596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5894.00i | 0.904007i | 0.892016 | + | 0.452004i | \(0.149291\pi\) | ||||
−0.892016 | + | 0.452004i | \(0.850709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 270.000 | 0.0410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11106.0 | 1.67454 | 0.837270 | − | 0.546789i | \(-0.184150\pi\) | ||||
0.837270 | + | 0.546789i | \(0.184150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6480.00i | − 0.968796i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 432.000i | − 0.0640444i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13176.0 | 1.93705 | 0.968527 | − | 0.248907i | \(-0.0800713\pi\) | ||||
0.968527 | + | 0.248907i | \(0.0800713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3141.00 | −0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 105.000i | − 0.0151820i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 468.000i | − 0.0671130i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6112.00 | 0.869329 | 0.434665 | − | 0.900592i | \(-0.356867\pi\) | ||||
0.434665 | + | 0.900592i | \(0.356867\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 810.000 | 0.114273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3312.00i | − 0.463478i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13618.0i | 1.89038i | 0.326515 | + | 0.945192i | \(0.394126\pi\) | ||||
−0.326515 | + | 0.945192i | \(0.605874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3996.00 | −0.550273 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2340.00 | −0.319671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 692.000i | 0.0937880i | 0.998900 | + | 0.0468940i | \(0.0149323\pi\) | ||||
−0.998900 | + | 0.0468940i | \(0.985068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1776.00i | − 0.238812i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8064.00 | 1.07585 | 0.537926 | − | 0.842992i | \(-0.319208\pi\) | ||||
0.537926 | + | 0.842992i | \(0.319208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5184.00 | −0.686237 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4068.00i | − 0.534336i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12654.0i | − 1.64931i | −0.565633 | − | 0.824657i | \(-0.691368\pi\) | ||||
0.565633 | − | 0.824657i | \(-0.308632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1296.00 | 0.167625 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5724.00 | 0.734701 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 9216.00i | − 1.17394i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 106.000i | − 0.0134005i | −0.999978 | − | 0.00670024i | \(-0.997867\pi\) | ||||
0.999978 | − | 0.00670024i | \(-0.00213277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2400.00 | 0.301129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4014.00 | −0.499874 | −0.249937 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249937 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 160.000i | − 0.0197771i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1458.00i | 0.178885i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8136.00 | −0.990876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3914.00 | −0.473190 | −0.236595 | − | 0.971608i | \(-0.576032\pi\) | ||||
−0.236595 | + | 0.971608i | \(0.576032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2862.00i | 0.343484i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5472.00i | − 0.651960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21384.0 | −2.52940 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7692.00 | 0.903307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 4428.00i | − 0.516282i | −0.966107 | − | 0.258141i | \(-0.916890\pi\) | ||||
0.966107 | − | 0.258141i | \(-0.0831098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15490.0i | 1.79320i | 0.442843 | + | 0.896599i | \(0.353970\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3888.00 | 0.446906 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3582.00 | −0.408829 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3376.00i | 0.382614i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1080.00i | − 0.121545i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6768.00 | −0.756388 | −0.378194 | − | 0.925726i | \(-0.623455\pi\) | ||||
−0.378194 | + | 0.925726i | \(0.623455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1298.00 | 0.144060 | 0.0720299 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720299 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 12636.0i | − 1.39276i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7200.00i | 0.788153i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2248.00 | −0.244399 | −0.122200 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122200 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2511.00 | 0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9612.00i | − 1.03088i | −0.856926 | − | 0.515440i | \(-0.827628\pi\) | ||||
0.856926 | − | 0.515440i | \(-0.172372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11340.0i | 1.20802i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2214.00 | 0.234270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 162.000 | 0.0170273 | 0.00851364 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851364 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3240.00i | − 0.338283i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7320.00i | 0.759213i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1440.00 | 0.148370 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1370.00 | −0.140232 | −0.0701159 | − | 0.997539i | \(-0.522337\pi\) | ||||
−0.0701159 | + | 0.997539i | \(0.522337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 486.000i | 0.0494217i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 15354.0i | − 1.55121i | −0.631220 | − | 0.775604i | \(-0.717445\pi\) | ||||
0.631220 | − | 0.775604i | \(-0.282555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13024.0 | 1.30729 | 0.653646 | − | 0.756800i | \(-0.273238\pi\) | ||||
0.653646 | + | 0.756800i | \(0.273238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 864.000 | 0.0861657 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14436.0i | 1.43045i | 0.698896 | + | 0.715223i | \(0.253675\pi\) | ||||
−0.698896 | + | 0.715223i | \(0.746325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2656.00i | − 0.261498i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7662.00 | −0.749568 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16272.0 | −1.58179 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 19900.0i | − 1.92226i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00i | 0.357656i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12096.0 | −1.15382 | −0.576911 | − | 0.816807i | \(-0.695742\pi\) | ||||
−0.576911 | + | 0.816807i | \(0.695742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2260.00 | 0.214235 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1728.00i | − 0.162788i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 18972.0i | − 1.77624i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6056.00 | 0.563498 | 0.281749 | − | 0.959488i | \(-0.409085\pi\) | ||||
0.281749 | + | 0.959488i | \(0.409085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2460.00 | 0.227495 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7524.00i | 0.691555i | 0.938317 | + | 0.345777i | \(0.112385\pi\) | ||||
−0.938317 | + | 0.345777i | \(0.887615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4212.00i | − 0.384785i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5832.00 | 0.529553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2880.00 | −0.259931 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5276.00i | − 0.473319i | −0.971593 | − | 0.236660i | \(-0.923947\pi\) | ||||
0.971593 | − | 0.236660i | \(-0.0760526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5832.00i | − 0.520069i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4968.00 | 0.440382 | 0.220191 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220191 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10044.0 | 0.885054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6291.00i | − 0.551071i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10998.0i | 0.957717i | 0.877892 | + | 0.478858i | \(0.158949\pi\) | ||||
−0.877892 | + | 0.478858i | \(0.841051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −208.000 | −0.0180066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2700.00 | −0.232374 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 144.000i | 0.0123212i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 15552.0i | − 1.32297i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3726.00 | −0.315131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8838.00 | 0.743186 | 0.371593 | − | 0.928396i | \(-0.378812\pi\) | ||||
0.371593 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22436.0i | 1.87583i | 0.346869 | + | 0.937914i | \(0.387245\pi\) | ||||
−0.346869 | + | 0.937914i | \(0.612755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4776.00i | 0.397032i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 288.000 | 0.0238055 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6156.00i | 0.503103i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 900.000i | 0.0731395i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31752.0 | −2.56590 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3348.00 | −0.269044 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 10044.0i | − 0.802645i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4762.00i | − 0.378437i | −0.981935 | − | 0.189218i | \(-0.939405\pi\) | ||||
0.981935 | − | 0.189218i | \(-0.0605954\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3210.00 | −0.253691 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29196.0 | −2.29471 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6004.00i | 0.469310i | 0.972079 | + | 0.234655i | \(0.0753960\pi\) | ||||
−0.972079 | + | 0.234655i | \(0.924604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3798.00i | − 0.295254i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23400.0 | 1.80921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4096.00 | −0.314972 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12204.0i | 0.933389i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5274.00i | − 0.401197i | −0.979674 | − | 0.200598i | \(-0.935711\pi\) | ||||
0.979674 | − | 0.200598i | \(-0.0642886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4520.00 | 0.341996 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1944.00 | 0.146303 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12420.0i | 0.929735i | 0.885380 | + | 0.464867i | \(0.153898\pi\) | ||||
−0.885380 | + | 0.464867i | \(0.846102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 20412.0i | − 1.51989i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 648.000 | 0.0479955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21366.0 | 1.57418 | 0.787091 | − | 0.616837i | \(-0.211586\pi\) | ||||
0.787091 | + | 0.616837i | \(0.211586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21140.0i | 1.54935i | 0.632357 | + | 0.774677i | \(0.282088\pi\) | ||||
−0.632357 | + | 0.774677i | \(0.717912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1728.00i | − 0.125983i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14328.0 | −1.03916 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3266.00 | 0.235642 | 0.117821 | − | 0.993035i | \(-0.462409\pi\) | ||||
0.117821 | + | 0.993035i | \(0.462409\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4026.00i | 0.288972i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9504.00i | 0.678644i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14904.0 | 1.05877 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1620.00 | −0.114494 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17028.0i | 1.19731i | 0.801007 | + | 0.598655i | \(0.204298\pi\) | ||||
−0.801007 | + | 0.598655i | \(0.795702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1600.00i | 0.111930i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4266.00 | −0.296920 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9522.00 | 0.659396 | 0.329698 | − | 0.944086i | \(-0.393053\pi\) | ||||
0.329698 | + | 0.944086i | \(0.393053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2592.00i | 0.178591i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 2616.00i | − 0.179340i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10296.0 | −0.702309 | −0.351155 | − | 0.936318i | \(-0.614211\pi\) | ||||
−0.351155 | + | 0.936318i | \(0.614211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3382.00 | 0.229542 | 0.114771 | − | 0.993392i | \(-0.463387\pi\) | ||||
0.114771 | + | 0.993392i | \(0.463387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2988.00i | 0.201792i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 630.000i | 0.0423358i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20656.0 | 1.38122 | 0.690611 | − | 0.723227i | \(-0.257342\pi\) | ||||
0.690611 | + | 0.723227i | \(0.257342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5616.00 | −0.373681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4320.00i | 0.286037i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22114.0i | 1.45706i | 0.685015 | + | 0.728529i | \(0.259795\pi\) | ||||
−0.685015 | + | 0.728529i | \(0.740205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4860.00 | −0.318657 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19962.0 | −1.30250 | −0.651248 | − | 0.758865i | \(-0.725754\pi\) | ||||
−0.651248 | + | 0.758865i | \(0.725754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 604.000i | − 0.0392194i | −0.999808 | − | 0.0196097i | \(-0.993758\pi\) | ||||
0.999808 | − | 0.0196097i | \(-0.00624236\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1944.00i | 0.125620i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5040.00 | 0.324115 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10800.0i | 0.687895i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4068.00i | 0.257872i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 152.000 | 0.00958958 | 0.00479479 | − | 0.999989i | \(-0.498474\pi\) | ||||
0.00479479 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4020.00 | −0.252418 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10656.0i | 0.665938i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2790.00i | 0.173538i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3240.00 | 0.200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4194.00 | 0.258429 | 0.129215 | − | 0.991617i | \(-0.458754\pi\) | ||||
0.129215 | + | 0.991617i | \(0.458754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7252.00i | 0.444776i | 0.974958 | + | 0.222388i | \(0.0713852\pi\) | ||||
−0.974958 | + | 0.222388i | \(0.928615\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24408.0i | 1.49002i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6696.00 | −0.406873 | −0.203437 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203437 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24624.0 | 1.48933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 384.000i | − 0.0231185i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28422.0i | 1.70328i | 0.524131 | + | 0.851638i | \(0.324390\pi\) | ||||
−0.524131 | + | 0.851638i | \(0.675610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34344.0 | −2.04875 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 234.000 | 0.0138953 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19908.0i | 1.17679i | 0.808573 | + | 0.588396i | \(0.200240\pi\) | ||||
−0.808573 | + | 0.588396i | \(0.799760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14318.0i | − 0.842520i | −0.906940 | − | 0.421260i | \(-0.861588\pi\) | ||||
0.906940 | − | 0.421260i | \(-0.138412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −540.000 | −0.0316318 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14400.0 | −0.839711 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16848.0i | − 0.978047i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14640.0i | 0.846061i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15192.0 | −0.874040 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30050.0 | 1.72116 | 0.860581 | − | 0.509313i | \(-0.170101\pi\) | ||||
0.860581 | + | 0.509313i | \(0.170101\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5373.00i | − 0.306381i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 22158.0i | − 1.25790i | −0.777444 | − | 0.628952i | \(-0.783484\pi\) | ||||
0.777444 | − | 0.628952i | \(-0.216516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8432.00 | −0.476569 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8100.00 | −0.455790 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3132.00i | − 0.175465i | −0.996144 | − | 0.0877325i | \(-0.972038\pi\) | ||||
0.996144 | − | 0.0877325i | \(-0.0279621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 17172.0i | − 0.957822i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −762.000 | −0.0423175 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4140.00 | −0.228914 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20932.0i | 1.15237i | 0.817318 | + | 0.576187i | \(0.195460\pi\) | ||||
−0.817318 | + | 0.576187i | \(0.804540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2592.00i | − 0.142081i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46152.0 | −2.51891 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1620.00 | −0.0880371 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13230.0i | 0.715886i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 21834.0i | − 1.17640i | −0.808714 | − | 0.588202i | \(-0.799836\pi\) | ||||
0.808714 | − | 0.588202i | \(-0.200164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22600.0 | −1.21248 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23328.0 | −1.24622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4464.00i | − 0.237463i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 12446.0i | − 0.659266i | −0.944109 | − | 0.329633i | \(-0.893075\pi\) | ||||
0.944109 | − | 0.329633i | \(-0.106925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4608.00 | 0.243057 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1152.00 | 0.0605088 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6480.00i | 0.338935i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11664.0i | − 0.607531i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12528.0 | 0.649813 | 0.324907 | − | 0.945746i | \(-0.394667\pi\) | ||||
0.324907 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.0000 | 0.00330580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 15414.0i | − 0.792881i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46566.0i | 2.38540i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11576.0 | 0.590550 | 0.295275 | − | 0.955412i | \(-0.404589\pi\) | ||||
0.295275 | + | 0.955412i | \(0.404589\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8136.00i | 0.411656i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 29338.0i | − 1.47834i | −0.673519 | − | 0.739170i | \(-0.735218\pi\) | ||||
0.673519 | − | 0.739170i | \(-0.264782\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15066.0 | −0.756079 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11952.0 | 0.597364 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2540.00i | − 0.126435i | −0.998000 | − | 0.0632175i | \(-0.979864\pi\) | ||||
0.998000 | − | 0.0632175i | \(-0.0201362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 3000.00i | − 0.148728i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18792.0 | −0.927876 | −0.463938 | − | 0.885868i | \(-0.653564\pi\) | ||||
−0.463938 | + | 0.885868i | \(0.653564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13284.0 | −0.653273 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10692.0i | − 0.523695i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14112.0i | 0.688440i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4832.00 | −0.234783 | −0.117392 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117392 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14364.0 | 0.695157 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 43920.0i | − 2.11710i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20818.0i | 0.999529i | 0.866161 | + | 0.499764i | \(0.166580\pi\) | ||||
−0.866161 | + | 0.499764i | \(0.833420\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7776.00 | 0.371872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12042.0 | −0.573617 | −0.286808 | − | 0.957988i | \(-0.592594\pi\) | ||||
−0.286808 | + | 0.957988i | \(0.592594\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12976.0i | 0.615679i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2916.00i | − 0.137815i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6840.00 | −0.322005 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13058.0 | 0.612332 | 0.306166 | − | 0.951978i | \(-0.400954\pi\) | ||||
0.306166 | + | 0.951978i | \(0.400954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17658.0i | 0.824821i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11826.0i | 0.550261i | 0.961407 | + | 0.275130i | \(0.0887210\pi\) | ||||
−0.961407 | + | 0.275130i | \(0.911279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3184.00 | −0.147578 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5424.00 | 0.250431 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 9000.00i | − 0.413939i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 12960.0i | − 0.593784i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6318.00 | 0.288361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45972.0 | 2.09021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 11996.0i | − 0.543343i | −0.962390 | − | 0.271672i | \(-0.912424\pi\) | ||||
0.962390 | − | 0.271672i | \(-0.0875765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 6696.00i | − 0.302134i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9072.00 | −0.407792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4220.00 | 0.188974 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 22356.0i | − 0.997340i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6966.00i | 0.309596i | 0.987946 | + | 0.154798i | \(0.0494727\pi\) | ||||
−0.987946 | + | 0.154798i | \(0.950527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7776.00 | −0.344299 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5670.00 | −0.250112 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 936.000i | − 0.0411342i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10368.0i | 0.453943i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1998.00 | −0.0871536 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40806.0 | 1.77338 | 0.886689 | − | 0.462367i | \(-0.153000\pi\) | ||||
0.886689 | + | 0.462367i | \(0.153000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 17980.0i | − 0.778500i | −0.921132 | − | 0.389250i | \(-0.872734\pi\) | ||||
0.921132 | − | 0.389250i | \(-0.127266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16608.0i | − 0.716443i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14760.0 | −0.634381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45200.0 | −1.93555 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 720.000i | 0.0307190i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12834.0i | 0.545566i | 0.962076 | + | 0.272783i | \(0.0879441\pi\) | ||||
−0.962076 | + | 0.272783i | \(0.912056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37864.0 | −1.60371 | −0.801857 | − | 0.597516i | \(-0.796154\pi\) | ||||
−0.801857 | + | 0.597516i | \(0.796154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21492.0 | −0.906976 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42516.0i | 1.78770i | 0.448368 | + | 0.893849i | \(0.352005\pi\) | ||||
−0.448368 | + | 0.893849i | \(0.647995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45638.0i | 1.91203i | 0.293317 | + | 0.956015i | \(0.405241\pi\) | ||||
−0.293317 | + | 0.956015i | \(0.594759\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6378.00 | −0.266246 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5022.00 | −0.208886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34992.0i | 1.45024i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 432.000i | 0.0178400i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17496.0 | 0.719939 | 0.359970 | − | 0.932964i | \(-0.382787\pi\) | ||||
0.359970 | + | 0.932964i | \(0.382787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30367.0 | −1.24511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8802.00i | − 0.359617i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37746.0i | 1.53669i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 280.000 | 0.0113588 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6108.00 | 0.246909 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16272.0i | 0.655461i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 32174.0i | − 1.29146i | −0.763565 | − | 0.645731i | \(-0.776553\pi\) | ||||
0.763565 | − | 0.645731i | \(-0.223447\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16200.0 | 0.647986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38934.0 | 1.55188 | 0.775939 | − | 0.630807i | \(-0.217276\pi\) | ||||
0.775939 | + | 0.630807i | \(0.217276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29780.0i | 1.18286i | 0.806355 | + | 0.591432i | \(0.201437\pi\) | ||||
−0.806355 | + | 0.591432i | \(0.798563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2160.00i | 0.0854966i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48096.0 | 1.89711 | 0.948556 | − | 0.316611i | \(-0.102545\pi\) | ||||
0.948556 | + | 0.316611i | \(0.102545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22356.0 | 0.878759 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13767.0i | 0.539275i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 18432.0i | − 0.719520i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3320.00 | −0.129155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9486.00 | 0.367758 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 10656.0i | − 0.411701i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21302.0i | 0.820202i | 0.912040 | + | 0.410101i | \(0.134507\pi\) | ||||
−0.912040 | + | 0.410101i | \(0.865493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6858.00 | −0.263157 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7470.00 | −0.285665 | −0.142832 | − | 0.989747i | \(-0.545621\pi\) | ||||
−0.142832 | + | 0.989747i | \(0.545621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 764.000i | − 0.0291174i | −0.999894 | − | 0.0145587i | \(-0.995366\pi\) | ||||
0.999894 | − | 0.0145587i | \(-0.00463434\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 36936.0i | − 1.40293i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32328.0 | 1.22375 | 0.611876 | − | 0.790954i | \(-0.290415\pi\) | ||||
0.611876 | + | 0.790954i | \(0.290415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4736.00 | 0.178673 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00i | 0.109640i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 43200.0i | − 1.61885i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20088.0 | 0.750243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2160.00 | −0.0804017 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3744.00i | − 0.138898i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 7452.00i | − 0.275541i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10848.0 | 0.399777 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19260.0 | 0.707430 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 36316.0i | − 1.32950i | −0.747068 | − | 0.664748i | \(-0.768539\pi\) | ||||
0.747068 | − | 0.664748i | \(-0.231461\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5022.00i | 0.183244i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13392.0 | 0.487044 | 0.243522 | − | 0.969895i | \(-0.421697\pi\) | ||||
0.243522 | + | 0.969895i | \(0.421697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42768.0 | −1.55029 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22788.0i | 0.823331i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15264.0i | 0.549686i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38072.0 | 1.36657 | 0.683286 | − | 0.730151i | \(-0.260550\pi\) | ||||
0.683286 | + | 0.730151i | \(0.260550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3732.00 | −0.133522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3600.00i | 0.128381i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 44974.0i | − 1.59863i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −72.0000 | −0.00255101 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12798.0 | −0.451979 | −0.225990 | − | 0.974130i | \(-0.572562\pi\) | ||||
−0.225990 | + | 0.974130i | \(0.572562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 27900.0i | − 0.982154i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3672.00i | − 0.128849i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11664.0 | −0.407972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34874.0 | −1.21588 | −0.607942 | − | 0.793981i | \(-0.708005\pi\) | ||||
−0.607942 | + | 0.793981i | \(0.708005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5694.00i | 0.197888i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17190.0i | 0.595513i | 0.954642 | + | 0.297757i | \(0.0962384\pi\) | ||||
−0.954642 | + | 0.297757i | \(0.903762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6480.00 | −0.223773 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3888.00 | −0.133838 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 40284.0i | − 1.38232i | −0.722703 | − | 0.691158i | \(-0.757101\pi\) | ||||
0.722703 | − | 0.691158i | \(-0.242899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 260.000i | 0.00889353i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27486.0 | −0.937218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15498.0 | −0.526789 | −0.263394 | − | 0.964688i | \(-0.584842\pi\) | ||||
−0.263394 | + | 0.964688i | \(0.584842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10368.0i | 0.351310i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 25272.0i | − 0.853634i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7632.00 | −0.256987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29535.0 | −0.991407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 15876.0i | − 0.531253i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 24156.0i | − 0.805813i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37160.0 | 1.23577 | 0.617883 | − | 0.786270i | \(-0.287991\pi\) | ||||
0.617883 | + | 0.786270i | \(0.287991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5400.00 | 0.179023 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18468.0i | 0.610367i | 0.952294 | + | 0.305183i | \(0.0987178\pi\) | ||||
−0.952294 | + | 0.305183i | \(0.901282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20512.0i | 0.675832i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5970.00 | 0.196095 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10386.0 | 0.340100 | 0.170050 | − | 0.985435i | \(-0.445607\pi\) | ||||
0.170050 | + | 0.985435i | \(0.445607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22680.0i | 0.740404i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 14598.0i | − 0.475105i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44136.0 | 1.43206 | 0.716032 | − | 0.698067i | \(-0.245956\pi\) | ||||
0.716032 | + | 0.698067i | \(0.245956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25596.0 | 0.827976 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10368.0i | 0.334364i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32544.0i | 1.04635i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28432.0 | 0.911375 | 0.455687 | − | 0.890140i | \(-0.349394\pi\) | ||||
0.455687 | + | 0.890140i | \(0.349394\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13044.0 | −0.416857 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15696.0i | 0.500097i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39778.0i | 1.26357i | 0.775143 | + | 0.631786i | \(0.217678\pi\) | ||||
−0.775143 | + | 0.631786i | \(0.782322\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6102.00 | −0.193252 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))