Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2028,4,Mod(337,2028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2028.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2028.b (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: | \(119.655873492\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2028.337 |
Dual form | 2028.4.b.c.337.1 |
$q$-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 \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1015\) | \(1861\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.0000i | 1.60997i | 0.593296 | + | 0.804984i | \(0.297826\pi\) | ||||
−0.593296 | + | 0.804984i | \(0.702174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000i | 0.431959i | 0.976398 | + | 0.215980i | \(0.0692945\pi\) | ||||
−0.976398 | + | 0.215980i | \(0.930705\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000i | 0.929516i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.0000 | −0.256802 | −0.128401 | − | 0.991722i | \(-0.540985\pi\) | ||||
−0.128401 | + | 0.991722i | \(0.540985\pi\) | |||||||
\(18\) | 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 | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −199.000 | −1.59200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −234.000 | −1.49837 | −0.749185 | − | 0.662361i | \(-0.769554\pi\) | ||||
−0.749185 | + | 0.662361i | \(0.769554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.0000i | 0.0926995i | 0.998925 | + | 0.0463498i | \(0.0147589\pi\) | ||||
−0.998925 | + | 0.0463498i | \(0.985241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 108.000i | 0.569709i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −144.000 | −0.695441 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 226.000i | − 1.00417i | −0.864819 | − | 0.502083i | \(-0.832567\pi\) | ||||
0.864819 | − | 0.502083i | \(-0.167433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 90.0000i | − 0.342820i | −0.985200 | − | 0.171410i | \(-0.945168\pi\) | ||||
0.985200 | − | 0.171410i | \(-0.0548323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −452.000 | −1.60301 | −0.801504 | − | 0.597989i | \(-0.795967\pi\) | ||||
−0.801504 | + | 0.597989i | \(0.795967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 162.000i | 0.536656i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 432.000i | 1.34072i | 0.742038 | + | 0.670358i | \(0.233860\pi\) | ||||
−0.742038 | + | 0.670358i | \(0.766140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 279.000 | 0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −54.0000 | −0.148265 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −648.000 | −1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 300.000i | 0.697122i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 684.000i | − 1.50931i | −0.656123 | − | 0.754654i | \(-0.727805\pi\) | ||||
0.656123 | − | 0.754654i | \(-0.272195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 422.000 | 0.885763 | 0.442882 | − | 0.896580i | \(-0.353956\pi\) | ||||
0.442882 | + | 0.896580i | \(0.353956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 72.0000i | 0.143986i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 332.000i | − 0.605377i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) | ||||
0.953090 | − | 0.302688i | \(-0.0978842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 360.000i | 0.601748i | 0.953664 | + | 0.300874i | \(0.0972784\pi\) | ||||
−0.953664 | + | 0.300874i | \(0.902722\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26.0000i | 0.0416859i | 0.999783 | + | 0.0208429i | \(0.00663500\pi\) | ||||
−0.999783 | + | 0.0208429i | \(0.993365\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −597.000 | −0.919142 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −288.000 | −0.426242 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 512.000 | 0.729171 | 0.364585 | − | 0.931170i | \(-0.381211\pi\) | ||||
0.364585 | + | 0.931170i | \(0.381211\pi\) | |||||||
\(80\) | 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 | ||||||||
\(89\) | − 630.000i | − 0.750336i | −0.926957 | − | 0.375168i | \(-0.877585\pi\) | ||||
0.926957 | − | 0.375168i | \(-0.122415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.0000i | 0.0535201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1800.00 | −1.94396 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1054.00i | 1.10327i | 0.834085 | + | 0.551637i | \(0.185996\pi\) | ||||
−0.834085 | + | 0.551637i | \(0.814004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000i | 0.328921i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −558.000 | −0.549733 | −0.274867 | − | 0.961482i | \(-0.588634\pi\) | ||||
−0.274867 | + | 0.961482i | \(0.588634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.00765304 | −0.00382652 | − | 0.999993i | \(-0.501218\pi\) | ||||
−0.00382652 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −432.000 | −0.401513 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1764.00 | 1.59376 | 0.796880 | − | 0.604138i | \(-0.206482\pi\) | ||||
0.796880 | + | 0.604138i | \(0.206482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1622.00i | − 1.42532i | −0.701512 | − | 0.712658i | \(-0.747491\pi\) | ||||
0.701512 | − | 0.712658i | \(-0.252509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 678.000i | − 0.579756i | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 144.000i | − 0.110928i | ||||||||
\(120\) | 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 | ||||||||
\(131\) | −1908.00 | −1.27254 | −0.636270 | − | 0.771466i | \(-0.719524\pi\) | ||||
−0.636270 | + | 0.771466i | \(0.719524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −800.000 | −0.521570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 486.000i | 0.309839i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 954.000i | 0.594932i | 0.954732 | + | 0.297466i | \(0.0961415\pi\) | ||||
−0.954732 | + | 0.297466i | \(0.903858\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2564.00 | 1.56457 | 0.782286 | − | 0.622919i | \(-0.214053\pi\) | ||||
0.782286 | + | 0.622919i | \(0.214053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1296.00i | 0.774063i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 4212.00i | − 2.41233i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 837.000 | 0.469623 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 738.000i | 0.405767i | 0.979203 | + | 0.202884i | \(0.0650313\pi\) | ||||
−0.979203 | + | 0.202884i | \(0.934969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2440.00i | − 1.31500i | −0.753456 | − | 0.657498i | \(-0.771615\pi\) | ||||
0.753456 | − | 0.657498i | \(-0.228385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −162.000 | −0.0856008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −288.000 | −0.149243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2554.00 | −1.29829 | −0.649145 | − | 0.760665i | \(-0.724873\pi\) | ||||
−0.649145 | + | 0.760665i | \(0.724873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1242.00 | 0.619478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 576.000i | − 0.281958i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 820.000i | − 0.394033i | −0.980400 | − | 0.197016i | \(-0.936875\pi\) | ||||
0.980400 | − | 0.197016i | \(-0.0631252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1944.00 | −0.917213 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1944.00i | 0.900786i | 0.892830 | + | 0.450393i | \(0.148716\pi\) | ||||
−0.892830 | + | 0.450393i | \(0.851284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 900.000i | 0.402484i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1242.00 | 0.545824 | 0.272912 | − | 0.962039i | \(-0.412013\pi\) | ||||
0.272912 | + | 0.962039i | \(0.412013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1592.00i | − 0.687679i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2052.00i | − 0.871400i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1116.00 | −0.465999 | −0.232999 | − | 0.972477i | \(-0.574854\pi\) | ||||
−0.232999 | + | 0.972477i | \(0.574854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1070.00 | −0.439406 | −0.219703 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219703 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(182\) | 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 | \(-0.534798\pi\) | ||||
−0.109104 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1342.00i | − 0.500514i | −0.968179 | − | 0.250257i | \(-0.919485\pi\) | ||||
0.968179 | − | 0.250257i | \(-0.0805152\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | \(-0.549639\pi\) | ||||
−0.155313 | + | 0.987865i | \(0.549639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 996.000i | − 0.349515i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1872.00i | − 0.647235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1620.00 | 0.551930 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3600.00 | −1.19147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1340.00 | 0.437201 | 0.218600 | − | 0.975814i | \(-0.429851\pi\) | ||||
0.218600 | + | 0.975814i | \(0.429851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1080.00i | 0.347420i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 8136.00i | − 2.58079i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −128.000 | −0.0400424 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 78.0000i | 0.0240674i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4880.00i | − 1.46542i | −0.680540 | − | 0.732711i | \(-0.738255\pi\) | ||||
0.680540 | − | 0.732711i | \(-0.261745\pi\) | |||||||
\(224\) | 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 | \(0.0116680\pi\) | ||||
−0.999328 | + | 0.0366480i | \(0.988332\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | −7776.00 | −2.15851 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1536.00 | 0.420987 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3888.00i | 1.05228i | 0.850399 | + | 0.526138i | \(0.176360\pi\) | ||||
−0.850399 | + | 0.526138i | \(0.823640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5138.00i | 1.37331i | 0.726984 | + | 0.686655i | \(0.240922\pi\) | ||||
−0.726984 | + | 0.686655i | \(0.759078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5022.00i | 1.30957i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3564.00i | 0.907066i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4788.00 | −1.20405 | −0.602024 | − | 0.798478i | \(-0.705639\pi\) | ||||
−0.602024 | + | 0.798478i | \(0.705639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2592.00i | − 0.644101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 972.000i | − 0.238702i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5886.00 | 1.42863 | 0.714316 | − | 0.699823i | \(-0.246738\pi\) | ||||
0.714316 | + | 0.699823i | \(0.246738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1808.00 | 0.433759 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2106.00 | −0.499456 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2232.00 | 0.523312 | 0.261656 | − | 0.965161i | \(-0.415731\pi\) | ||||
0.261656 | + | 0.965161i | \(0.415731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7452.00i | 1.72744i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1890.00i | − 0.433206i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −666.000 | −0.150954 | −0.0754772 | − | 0.997148i | \(-0.524048\pi\) | ||||
−0.0754772 | + | 0.997148i | \(0.524048\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 5536.00i | − 1.24092i | −0.784240 | − | 0.620458i | \(-0.786947\pi\) | ||||
0.784240 | − | 0.620458i | \(-0.213053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7164.00i | − 1.57093i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2126.00 | −0.461151 | −0.230576 | − | 0.973054i | \(-0.574061\pi\) | ||||
−0.230576 | + | 0.973054i | \(0.574061\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 144.000i | 0.0308998i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 2934.00i | − 0.622875i | −0.950267 | − | 0.311437i | \(-0.899190\pi\) | ||||
0.950267 | − | 0.311437i | \(-0.100810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2036.00 | −0.427659 | −0.213830 | − | 0.976871i | \(-0.568594\pi\) | ||||
−0.213830 | + | 0.976871i | \(0.568594\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5400.00 | −1.12235 | ||||||||
\(286\) | 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 | \(0.0731860\pi\) | ||||
−0.973684 | + | 0.227900i | \(0.926814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12312.0 | 2.42994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 972.000i | 0.189903i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3616.00i | − 0.692434i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1674.00 | −0.317389 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7596.00i | 1.42605i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1244.00i | 0.231267i | 0.993292 | + | 0.115633i | \(0.0368897\pi\) | ||||
−0.993292 | + | 0.115633i | \(0.963110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.0000 | −0.00441849 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1224.00 | −0.223173 | −0.111586 | − | 0.993755i | \(-0.535593\pi\) | ||||
−0.111586 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1898.00 | 0.342752 | 0.171376 | − | 0.985206i | \(-0.445179\pi\) | ||||
0.171376 | + | 0.985206i | \(0.445179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1296.00 | −0.231814 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9162.00i | 1.62331i | 0.584137 | + | 0.811655i | \(0.301433\pi\) | ||||
−0.584137 | + | 0.811655i | \(0.698567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8424.00i | − 1.47854i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5292.00 | 0.920158 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1800.00i | − 0.310076i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4866.00i | − 0.822906i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3456.00 | −0.579135 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4348.00i | 0.722017i | 0.932562 | + | 0.361009i | \(0.117568\pi\) | ||||
−0.932562 | + | 0.361009i | \(0.882432\pi\) | |||||||
\(332\) | 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 | \(-0.696243\pi\) | ||||
−0.578195 | + | 0.815899i | \(0.696243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3402.00 | −0.545048 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576.000 | −0.0914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4976.00i | 0.783320i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 3888.00i | − 0.606733i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1836.00 | −0.284039 | −0.142020 | − | 0.989864i | \(-0.545360\pi\) | ||||
−0.142020 | + | 0.989864i | \(0.545360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5894.00i | 0.904007i | 0.892016 | + | 0.452004i | \(0.149291\pi\) | ||||
−0.892016 | + | 0.452004i | \(0.850709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11106.0i | − 1.67454i | −0.546789 | − | 0.837270i | \(-0.684150\pi\) | ||||
0.546789 | − | 0.837270i | \(-0.315850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6480.00 | −0.968796 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 432.000i | − 0.0640444i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13176.0i | 1.93705i | 0.248907 | + | 0.968527i | \(0.419929\pi\) | ||||
−0.248907 | + | 0.968527i | \(0.580071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3141.00 | −0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −468.000 | −0.0671130 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6112.00 | −0.869329 | −0.434665 | − | 0.900592i | \(-0.643133\pi\) | ||||
−0.434665 | + | 0.900592i | \(0.643133\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 810.000i | − 0.114273i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3312.00i | 0.463478i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13618.0 | −1.89038 | −0.945192 | − | 0.326515i | \(-0.894126\pi\) | ||||
−0.945192 | + | 0.326515i | \(0.894126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 3996.00i | − 0.550273i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 692.000i | − 0.0937880i | −0.998900 | − | 0.0468940i | \(-0.985068\pi\) | ||||
0.998900 | − | 0.0468940i | \(-0.0149323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1776.00 | 0.238812 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8064.00i | 1.07585i | 0.842992 | + | 0.537926i | \(0.180792\pi\) | ||||
−0.842992 | + | 0.537926i | \(0.819208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 5184.00i | − 0.686237i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4068.00 | −0.534336 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12654.0 | −1.64931 | −0.824657 | − | 0.565633i | \(-0.808632\pi\) | ||||
−0.824657 | + | 0.565633i | \(0.808632\pi\) | |||||||
\(390\) | 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 | ||||||||
\(401\) | − 4014.00i | − 0.499874i | −0.968262 | − | 0.249937i | \(-0.919590\pi\) | ||||
0.968262 | − | 0.249937i | \(-0.0804100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1458.00i | 0.178885i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8136.00 | 0.990876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 3914.00i | − 0.473190i | −0.971608 | − | 0.236595i | \(-0.923968\pi\) | ||||
0.971608 | − | 0.236595i | \(-0.0760315\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2862.00i | 0.343484i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5472.00 | 0.651960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21384.0 | −2.52940 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7692.00 | 0.903307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4428.00 | 0.516282 | 0.258141 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258141 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15490.0i | 1.79320i | 0.442843 | + | 0.896599i | \(0.353970\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3888.00i | 0.446906i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3582.00 | 0.408829 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3376.00i | 0.382614i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 6768.00i | − 0.756388i | −0.925726 | − | 0.378194i | \(-0.876545\pi\) | ||||
0.925726 | − | 0.378194i | \(-0.123455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1298.00 | −0.144060 | −0.0720299 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720299 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(434\) | 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 | \(-0.461005\pi\) | ||||
0.122200 | + | 0.992506i | \(0.461005\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2511.00 | 0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9612.00 | −1.03088 | −0.515440 | − | 0.856926i | \(-0.672372\pi\) | ||||
−0.515440 | + | 0.856926i | \(0.672372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11340.0 | 1.20802 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2214.00i | 0.234270i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 162.000i | 0.0170273i | 0.999964 | + | 0.00851364i | \(0.00271001\pi\) | ||||
−0.999964 | + | 0.00851364i | \(0.997290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3240.00 | 0.338283 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7320.00i | − 0.759213i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1370.00i | − 0.140232i | −0.997539 | − | 0.0701159i | \(-0.977663\pi\) | ||||
0.997539 | − | 0.0701159i | \(-0.0223369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −486.000 | −0.0494217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15354.0i | 1.55121i | 0.631220 | + | 0.775604i | \(0.282555\pi\) | ||||
−0.631220 | + | 0.775604i | \(0.717445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 13024.0i | − 1.30729i | −0.756800 | − | 0.653646i | \(-0.773238\pi\) | ||||
0.756800 | − | 0.653646i | \(-0.226762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −864.000 | −0.0861657 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14436.0 | 1.43045 | 0.715223 | − | 0.698896i | \(-0.246325\pi\) | ||||
0.715223 | + | 0.698896i | \(0.246325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2656.00 | 0.261498 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7662.00 | −0.749568 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 16272.0i | − 1.58179i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 19900.0i | − 1.92226i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00 | 0.357656 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12096.0i | 1.15382i | 0.816807 | + | 0.576911i | \(0.195742\pi\) | ||||
−0.816807 | + | 0.576911i | \(0.804258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1728.00i | − 0.162788i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18972.0 | −1.77624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6056.00i | − 0.563498i | −0.959488 | − | 0.281749i | \(-0.909085\pi\) | ||||
0.959488 | − | 0.281749i | \(-0.0909146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 2460.00i | − 0.227495i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7524.00 | −0.691555 | −0.345777 | − | 0.938317i | \(-0.612385\pi\) | ||||
−0.345777 | + | 0.938317i | \(0.612385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4212.00 | 0.384785 | ||||||||
\(494\) | 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 | ||||||||
\(505\) | − 10044.0i | − 0.885054i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 10998.0i | − 0.957717i | −0.877892 | − | 0.478858i | \(-0.841051\pi\) | ||||
0.877892 | − | 0.478858i | \(-0.158949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −208.000 | −0.0180066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2700.00i | 0.232374i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 144.000i | − 0.0123212i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15552.0 | −1.32297 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3726.00 | 0.315131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8838.00 | −0.743186 | −0.371593 | − | 0.928396i | \(-0.621188\pi\) | ||||
−0.371593 | + | 0.928396i | \(0.621188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22436.0 | 1.87583 | 0.937914 | − | 0.346869i | \(-0.112755\pi\) | ||||
0.937914 | + | 0.346869i | \(0.112755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4776.00i | − 0.397032i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 288.000i | − 0.0238055i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6156.00i | − 0.503103i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31752.0i | 2.56590i | ||||||||
\(536\) | 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 | ||||||||
\(547\) | −6004.00 | −0.469310 | −0.234655 | − | 0.972079i | \(-0.575396\pi\) | ||||
−0.234655 | + | 0.972079i | \(0.575396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3798.00 | 0.295254 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 23400.0i | − 1.80921i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4096.00i | 0.314972i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12204.0 | 0.933389 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5274.00i | − 0.401197i | −0.979674 | − | 0.200598i | \(-0.935711\pi\) | ||||
0.979674 | − | 0.200598i | \(-0.0642886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − 1944.00i | − 0.146303i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12420.0 | 0.929735 | 0.464867 | − | 0.885380i | \(-0.346102\pi\) | ||||
0.464867 | + | 0.885380i | \(0.346102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 20412.0i | − 1.51989i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 648.000i | 0.0479955i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21366.0 | 1.57418 | 0.787091 | − | 0.616837i | \(-0.211586\pi\) | ||||
0.787091 | + | 0.616837i | \(0.211586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21140.0 | −1.54935 | −0.774677 | − | 0.632357i | \(-0.782088\pi\) | ||||
−0.774677 | + | 0.632357i | \(0.782088\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1728.00 | −0.125983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14328.0 | 1.03916 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3266.00i | − 0.235642i | −0.993035 | − | 0.117821i | \(-0.962409\pi\) | ||||
0.993035 | − | 0.117821i | \(-0.0375909\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4026.00i | − 0.288972i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9504.00 | −0.678644 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14904.0i | 1.05877i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 17028.0i | − 1.19731i | −0.801007 | − | 0.598655i | \(-0.795702\pi\) | ||||
0.801007 | − | 0.598655i | \(-0.204298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1600.00 | −0.111930 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 4266.00i | − 0.296920i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9522.00i | 0.659396i | 0.944086 | + | 0.329698i | \(0.106947\pi\) | ||||
−0.944086 | + | 0.329698i | \(0.893053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2592.00 | 0.178591 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2616.00 | −0.179340 | ||||||||
\(598\) | 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 | \(-0.536613\pi\) | ||||
−0.114771 | + | 0.993392i | \(0.536613\pi\) | |||||||
\(602\) | 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 | \(-0.742658\pi\) | ||||
−0.690611 | + | 0.723227i | \(0.742658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − 5616.00i | − 0.373681i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 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 | ||||||||
\(617\) | − 19962.0i | − 1.30250i | −0.758865 | − | 0.651248i | \(-0.774246\pi\) | ||||
0.758865 | − | 0.651248i | \(-0.225754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 604.000i | − 0.0392194i | −0.999808 | − | 0.0196097i | \(-0.993758\pi\) | ||||
0.999808 | − | 0.0196097i | \(-0.00624236\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5040.00 | 0.324115 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10800.0 | −0.687895 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4068.00i | 0.257872i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 152.000i | 0.00958958i | 0.999989 | + | 0.00479479i | \(0.00152623\pi\) | ||||
−0.999989 | + | 0.00479479i | \(0.998474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4020.00 | 0.252418 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10656.0i | 0.665938i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3240.00i | 0.200583i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4194.00 | −0.258429 | −0.129215 | − | 0.991617i | \(-0.541246\pi\) | ||||
−0.129215 | + | 0.991617i | \(0.541246\pi\) | |||||||
\(642\) | 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 | \(-0.434789\pi\) | ||||
0.203437 | + | 0.979088i | \(0.434789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24624.0 | 1.48933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −384.000 | −0.0231185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28422.0 | 1.70328 | 0.851638 | − | 0.524131i | \(-0.175610\pi\) | ||||
0.851638 | + | 0.524131i | \(0.175610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 34344.0i | − 2.04875i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 234.000i | 0.0138953i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19908.0 | −1.17679 | −0.588396 | − | 0.808573i | \(-0.700240\pi\) | ||||
−0.588396 | + | 0.808573i | \(0.700240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14318.0i | 0.842520i | 0.906940 | + | 0.421260i | \(0.138412\pi\) | ||||
−0.906940 | + | 0.421260i | \(0.861588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 14400.0i | − 0.839711i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16848.0 | 0.978047 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 14640.0i | − 0.846061i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15192.0i | 0.874040i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30050.0 | −1.72116 | −0.860581 | − | 0.509313i | \(-0.829899\pi\) | ||||
−0.860581 | + | 0.509313i | \(0.829899\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5373.00 | −0.306381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22158.0 | 1.25790 | 0.628952 | − | 0.777444i | \(-0.283484\pi\) | ||||
0.628952 | + | 0.777444i | \(0.283484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8432.00 | −0.476569 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − 8100.00i | − 0.455790i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3132.00i | − 0.175465i | −0.996144 | − | 0.0877325i | \(-0.972038\pi\) | ||||
0.996144 | − | 0.0877325i | \(-0.0279621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17172.0 | −0.957822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 762.000i | 0.0423175i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20932.0i | 1.15237i | 0.817318 | + | 0.576187i | \(0.195460\pi\) | ||||
−0.817318 | + | 0.576187i | \(0.804540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2592.00 | −0.142081 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46152.0i | 2.51891i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1620.00i | 0.0880371i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13230.0 | −0.715886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21834.0 | 1.17640 | 0.588202 | − | 0.808714i | \(-0.299836\pi\) | ||||
0.588202 | + | 0.808714i | \(0.299836\pi\) | |||||||
\(702\) | 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 | \(0.106925\pi\) | ||||
−0.944109 | + | 0.329633i | \(0.893075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4608.00 | 0.243057 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1152.00i | − 0.0605088i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(721\) | − 64.0000i | − 0.00330580i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15414.0i | 0.792881i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46566.0 | 2.38540 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11576.0 | −0.590550 | −0.295275 | − | 0.955412i | \(-0.595411\pi\) | ||||
−0.295275 | + | 0.955412i | \(0.595411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8136.00 | 0.411656 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29338.0i | 1.47834i | 0.673519 | + | 0.739170i | \(0.264782\pi\) | ||||
−0.673519 | + | 0.739170i | \(0.735218\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15066.0i | 0.756079i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11952.0 | 0.597364 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2540.00i | 0.126435i | 0.998000 | + | 0.0632175i | \(0.0201362\pi\) | ||||
−0.998000 | + | 0.0632175i | \(0.979864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18792.0i | 0.927876i | 0.885868 | + | 0.463938i | \(0.153564\pi\) | ||||
−0.885868 | + | 0.463938i | \(0.846436\pi\) | |||||||
\(744\) | 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 | ||||||||
\(755\) | 43920.0 | 2.11710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20818.0 | −0.999529 | −0.499764 | − | 0.866161i | \(-0.666580\pi\) | ||||
−0.499764 | + | 0.866161i | \(0.666580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 7776.00i | − 0.371872i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12042.0i | 0.573617i | 0.957988 | + | 0.286808i | \(0.0925943\pi\) | ||||
−0.957988 | + | 0.286808i | \(0.907406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12976.0 | 0.615679 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2916.00i | − 0.137815i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 13058.0i | − 0.612332i | −0.951978 | − | 0.306166i | \(-0.900954\pi\) | ||||
0.951978 | − | 0.306166i | \(-0.0990463\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17658.0 | 0.824821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11826.0i | 0.550261i | 0.961407 | + | 0.275130i | \(0.0887210\pi\) | ||||
−0.961407 | + | 0.275130i | \(0.911279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3184.00i | − 0.147578i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5424.00 | 0.250431 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9000.00 | 0.413939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12960.0 | −0.593784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6318.00 | −0.288361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 45972.0i | − 2.09021i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11996.0i | 0.543343i | 0.962390 | + | 0.271672i | \(0.0875765\pi\) | ||||
−0.962390 | + | 0.271672i | \(0.912424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6696.00 | 0.302134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 9072.00i | − 0.407792i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22356.0i | 0.997340i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6966.00 | −0.309596 | −0.154798 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154798 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 7776.00i | − 0.344299i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 5670.00i | − 0.250112i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −936.000 | −0.0411342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10368.0 | 0.453943 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1998.00 | −0.0871536 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40806.0 | −1.77338 | −0.886689 | − | 0.462367i | \(-0.847000\pi\) | ||||
−0.886689 | + | 0.462367i | \(0.847000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17980.0i | 0.778500i | 0.921132 | + | 0.389250i | \(0.127266\pi\) | ||||
−0.921132 | + | 0.389250i | \(0.872734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16608.0i | − 0.716443i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14760.0 | 0.634381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 45200.0i | − 1.93555i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | \(-0.203846\pi\) | ||||
0.801857 | + | 0.597516i | \(0.203846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 21492.0i | − 0.906976i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42516.0i | 1.78770i | 0.448368 | + | 0.893849i | \(0.352005\pi\) | ||||
−0.448368 | + | 0.893849i | \(0.647995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45638.0 | −1.91203 | −0.956015 | − | 0.293317i | \(-0.905241\pi\) | ||||
−0.956015 | + | 0.293317i | \(0.905241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6378.00 | −0.266246 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5022.00 | −0.208886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34992.0 | −1.45024 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 432.000i | 0.0178400i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17496.0i | 0.719939i | 0.932964 | + | 0.359970i | \(0.117213\pi\) | ||||
−0.932964 | + | 0.359970i | \(0.882787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30367.0 | 1.24511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8802.00i | − 0.359617i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 280.000i | 0.0113588i | ||||||||
\(848\) | 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 | \(0.223447\pi\) | ||||
−0.763565 | + | 0.645731i | \(0.776553\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 29780.0 | 1.18286 | 0.591432 | − | 0.806355i | \(-0.298563\pi\) | ||||
0.591432 | + | 0.806355i | \(0.298563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2160.00 | 0.0854966 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48096.0i | 1.89711i | 0.316611 | + | 0.948556i | \(0.397455\pi\) | ||||
−0.316611 | + | 0.948556i | \(0.602545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22356.0i | 0.878759i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13767.0 | −0.539275 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18432.0i | 0.719520i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9486.00i | 0.367758i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10656.0 | 0.411701 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 21302.0i | − 0.820202i | −0.912040 | − | 0.410101i | \(-0.865493\pi\) | ||||
0.912040 | − | 0.410101i | \(-0.134507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6858.00i | 0.263157i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7470.00 | 0.285665 | 0.142832 | − | 0.989747i | \(-0.454379\pi\) | ||||
0.142832 | + | 0.989747i | \(0.454379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −764.000 | −0.0291174 | −0.0145587 | − | 0.999894i | \(-0.504634\pi\) | ||||
−0.0145587 | + | 0.999894i | \(0.504634\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36936.0 | 1.40293 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32328.0 | 1.22375 | 0.611876 | − | 0.790954i | \(-0.290415\pi\) | ||||
0.611876 | + | 0.790954i | \(0.290415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4736.00i | 0.178673i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00i | 0.109640i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43200.0 | −1.61885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 20088.0i | − 0.750243i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3744.00i | − 0.138898i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7452.00 | −0.275541 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 10848.0i | − 0.399777i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 19260.0i | − 0.707430i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36316.0 | 1.32950 | 0.664748 | − | 0.747068i | \(-0.268539\pi\) | ||||
0.664748 | + | 0.747068i | \(0.268539\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5022.00 | −0.183244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13392.0 | −0.487044 | −0.243522 | − | 0.969895i | \(-0.578303\pi\) | ||||
−0.243522 | + | 0.969895i | \(0.578303\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | 3732.00i | 0.133522i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44974.0i | 1.59863i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −72.0000 | −0.00255101 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12798.0i | 0.451979i | 0.974130 | + | 0.225990i | \(0.0725616\pi\) | ||||
−0.974130 | + | 0.225990i | \(0.927438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27900.0i | 0.982154i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3672.00 | −0.128849 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11664.0 | 0.407972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34874.0 | 1.21588 | 0.607942 | − | 0.793981i | \(-0.291995\pi\) | ||||
0.607942 | + | 0.793981i | \(0.291995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5694.00 | 0.197888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 17190.0i | − 0.595513i | −0.954642 | − | 0.297757i | \(-0.903762\pi\) | ||||
0.954642 | − | 0.297757i | \(-0.0962384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6480.00i | 0.223773i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3888.00 | −0.133838 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40284.0i | 1.38232i | 0.722703 | + | 0.691158i | \(0.242899\pi\) | ||||
−0.722703 | + | 0.691158i | \(0.757101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27486.0i | 0.937218i | ||||||||
\(952\) | 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 | ||||||||
\(963\) | 15876.0 | 0.531253 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24156.0 | 0.805813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 37160.0i | − 1.23577i | −0.786270 | − | 0.617883i | \(-0.787991\pi\) | ||||
0.786270 | − | 0.617883i | \(-0.212009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 5400.00i | − 0.179023i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18468.0 | 0.610367 | 0.305183 | − | 0.952294i | \(-0.401282\pi\) | ||||
0.305183 | + | 0.952294i | \(0.401282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20512.0i | 0.675832i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 10386.0i | − 0.340100i | −0.985435 | − | 0.170050i | \(-0.945607\pi\) | ||||
0.985435 | − | 0.170050i | \(-0.0543929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22680.0 | 0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 14598.0i | − 0.475105i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44136.0i | 1.43206i | 0.698067 | + | 0.716032i | \(0.254044\pi\) | ||||
−0.698067 | + | 0.716032i | \(0.745956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25596.0 | 0.827976 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10368.0 | −0.334364 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32544.0 | 1.04635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28432.0 | −0.911375 | −0.455687 | − | 0.890140i | \(-0.650606\pi\) | ||||
−0.455687 | + | 0.890140i | \(0.650606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13044.0i | 0.416857i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 15696.0i | − 0.500097i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39778.0 | −1.26357 | −0.631786 | − | 0.775143i | \(-0.717678\pi\) | ||||
−0.631786 | + | 0.775143i | \(0.717678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 6102.00i | − 0.193252i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))