Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,4,Mod(49,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, 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("300.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(17.7005730017\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.49 |
Dual form | 300.4.d.e.49.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 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 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000i | 0.213346i | 0.994294 | + | 0.106673i | \(0.0340198\pi\) | ||||
−0.994294 | + | 0.106673i | \(0.965980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000i | 0.256802i | 0.991722 | + | 0.128401i | \(0.0409845\pi\) | ||||
−0.991722 | + | 0.128401i | \(0.959015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.000 | 1.20745 | 0.603726 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603726 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000 | 0.249392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 72.0000i | − 0.652741i | −0.945242 | − | 0.326370i | \(-0.894174\pi\) | ||||
0.945242 | − | 0.326370i | \(-0.105826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 234.000 | 1.49837 | 0.749185 | − | 0.662361i | \(-0.230446\pi\) | ||||
0.749185 | + | 0.662361i | \(0.230446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0000 | −0.0926995 | −0.0463498 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463498 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 108.000i | − 0.569709i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 226.000i | − 1.00417i | −0.864819 | − | 0.502083i | \(-0.832567\pi\) | ||||
0.864819 | − | 0.502083i | \(-0.167433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0000 | 0.123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 90.0000 | 0.342820 | 0.171410 | − | 0.985200i | \(-0.445168\pi\) | ||||
0.171410 | + | 0.985200i | \(0.445168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 452.000i | − 1.60301i | −0.597989 | − | 0.801504i | \(-0.704033\pi\) | ||||
0.597989 | − | 0.801504i | \(-0.295967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(53\) | − 414.000i | − 1.07297i | −0.843911 | − | 0.536484i | \(-0.819752\pi\) | ||||
0.843911 | − | 0.536484i | \(-0.180248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 300.000i | − 0.697122i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 684.000 | 1.50931 | 0.754654 | − | 0.656123i | \(-0.227805\pi\) | ||||
0.754654 | + | 0.656123i | \(0.227805\pi\) | |||||||
\(60\) | 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 | \(0.0978842\pi\) | ||||
−0.953090 | + | 0.302688i | \(0.902116\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −360.000 | −0.601748 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 26.0000i | − 0.0416859i | −0.999783 | − | 0.0208429i | \(-0.993365\pi\) | ||||
0.999783 | − | 0.0208429i | \(-0.00663500\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 702.000i | − 0.865084i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 630.000 | 0.750336 | 0.375168 | − | 0.926957i | \(-0.377585\pi\) | ||||
0.375168 | + | 0.926957i | \(0.377585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.0000 | −0.0921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.0000i | 0.0535201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1054.00i | − 1.10327i | −0.834085 | − | 0.551637i | \(-0.814004\pi\) | ||||
0.834085 | − | 0.551637i | \(-0.185996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −324.000 | −0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 558.000 | 0.549733 | 0.274867 | − | 0.961482i | \(-0.411366\pi\) | ||||
0.274867 | + | 0.961482i | \(0.411366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.00000i | − 0.00765304i | −0.999993 | − | 0.00382652i | \(-0.998782\pi\) | ||||
0.999993 | − | 0.00382652i | \(-0.00121802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1764.00i | 1.59376i | 0.604138 | + | 0.796880i | \(0.293518\pi\) | ||||
−0.604138 | + | 0.796880i | \(0.706482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1622.00 | −1.42532 | −0.712658 | − | 0.701512i | \(-0.752509\pi\) | ||||
−0.712658 | + | 0.701512i | \(0.752509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −678.000 | −0.579756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1134.00i | 0.944051i | 0.881585 | + | 0.472025i | \(0.156477\pi\) | ||||
−0.881585 | + | 0.472025i | \(0.843523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 592.000i | − 0.413634i | −0.978380 | − | 0.206817i | \(-0.933690\pi\) | ||||
0.978380 | − | 0.206817i | \(-0.0663105\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 800.000i | 0.521570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 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 | \(-0.785947\pi\) | ||||
−0.782286 | + | 0.622919i | \(0.785947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1296.00 | 0.774063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 360.000i | 0.210522i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 837.000i | − 0.469623i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 738.000 | 0.405767 | 0.202884 | − | 0.979203i | \(-0.434969\pi\) | ||||
0.202884 | + | 0.979203i | \(0.434969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2440.00 | −1.31500 | −0.657498 | − | 0.753456i | \(-0.728385\pi\) | ||||
−0.657498 | + | 0.753456i | \(0.728385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 162.000i | − 0.0856008i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1944.00i | 0.900786i | 0.892830 | + | 0.450393i | \(0.148716\pi\) | ||||
−0.892830 | + | 0.450393i | \(0.851284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2097.00 | 0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −900.000 | −0.402484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1242.00i | 0.545824i | 0.962039 | + | 0.272912i | \(0.0879867\pi\) | ||||
−0.962039 | + | 0.272912i | \(0.912013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(-0.429491\pi\) | ||||
0.219703 | + | 0.975567i | \(0.429491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1266.00i | − 0.511396i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 648.000i | 0.253403i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −216.000 | −0.0831306 | ||||||||
\(190\) | 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 | \(0.0805152\pi\) | ||||
−0.968179 | + | 0.250257i | \(0.919485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1422.00i | 0.514281i | 0.966374 | + | 0.257140i | \(0.0827803\pi\) | ||||
−0.966374 | + | 0.257140i | \(0.917220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −872.000 | −0.310625 | −0.155313 | − | 0.987865i | \(-0.549639\pi\) | ||||
−0.155313 | + | 0.987865i | \(0.549639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 996.000 | 0.349515 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1872.00i | 0.647235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000i | 0.217580i | ||||||||
\(208\) | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 128.000i | − 0.0400424i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −78.0000 | −0.0240674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −180.000 | −0.0547878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4880.00i | − 1.46542i | −0.680540 | − | 0.732711i | \(-0.738255\pi\) | ||||
0.680540 | − | 0.732711i | \(-0.261745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2700.00i | 0.789451i | 0.918799 | + | 0.394725i | \(0.129160\pi\) | ||||
−0.918799 | + | 0.394725i | \(0.870840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −254.000 | −0.0732960 | −0.0366480 | − | 0.999328i | \(-0.511668\pi\) | ||||
−0.0366480 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 864.000 | 0.246091 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4410.00i | − 1.23995i | −0.784621 | − | 0.619976i | \(-0.787142\pi\) | ||||
0.784621 | − | 0.619976i | \(-0.212858\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1000.00i | 0.257605i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3564.00 | 0.907066 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4788.00 | 1.20405 | 0.602024 | − | 0.798478i | \(-0.294361\pi\) | ||||
0.602024 | + | 0.798478i | \(0.294361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2592.00i | − 0.644101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5886.00i | − 1.42863i | −0.699823 | − | 0.714316i | \(-0.746738\pi\) | ||||
0.699823 | − | 0.714316i | \(-0.253262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1808.00 | 0.433759 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2106.00 | −0.499456 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2232.00i | − 0.523312i | −0.965161 | − | 0.261656i | \(-0.915731\pi\) | ||||
0.965161 | − | 0.261656i | \(-0.0842686\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1890.00i | − 0.433206i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 666.000 | 0.150954 | 0.0754772 | − | 0.997148i | \(-0.475952\pi\) | ||||
0.0754772 | + | 0.997148i | \(0.475952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5536.00 | −1.24092 | −0.620458 | − | 0.784240i | \(-0.713053\pi\) | ||||
−0.620458 | + | 0.784240i | \(0.713053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 240.000i | 0.0532068i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2126.00i | 0.461151i | 0.973054 | + | 0.230576i | \(0.0740609\pi\) | ||||
−0.973054 | + | 0.230576i | \(0.925939\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 144.000 | 0.0308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2934.00 | −0.622875 | −0.311437 | − | 0.950267i | \(-0.600810\pi\) | ||||
−0.311437 | + | 0.950267i | \(0.600810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2036.00i | − 0.427659i | −0.976871 | − | 0.213830i | \(-0.931406\pi\) | ||||
0.976871 | − | 0.213830i | \(-0.0685938\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 720.000i | 0.148085i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4589.00 | 0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3162.00 | −0.636975 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2286.00i | − 0.455800i | −0.973684 | − | 0.227900i | \(-0.926814\pi\) | ||||
0.973684 | − | 0.227900i | \(-0.0731860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 972.000i | 0.189903i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 720.000 | 0.139260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3616.00 | 0.692434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1674.00i | − 0.317389i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 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 | \(-0.464407\pi\) | ||||
0.111586 | + | 0.993755i | \(0.464407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1898.00i | − 0.342752i | −0.985206 | − | 0.171376i | \(-0.945179\pi\) | ||||
0.985206 | − | 0.171376i | \(-0.0548213\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4866.00i | 0.822906i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3456.00 | −0.579135 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4348.00 | −0.722017 | −0.361009 | − | 0.932562i | \(-0.617568\pi\) | ||||
−0.361009 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2034.00i | 0.334722i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7154.00i | 1.15639i | 0.815899 | + | 0.578195i | \(0.196243\pi\) | ||||
−0.815899 | + | 0.578195i | \(0.803757\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1836.00i | − 0.284039i | −0.989864 | − | 0.142020i | \(-0.954640\pi\) | ||||
0.989864 | − | 0.142020i | \(-0.0453596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5894.00 | −0.904007 | −0.452004 | − | 0.892016i | \(-0.649291\pi\) | ||||
−0.452004 | + | 0.892016i | \(0.649291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −270.000 | −0.0410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11106.0i | − 1.67454i | −0.546789 | − | 0.837270i | \(-0.684150\pi\) | ||||
0.546789 | − | 0.837270i | \(-0.315850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 432.000i | 0.0640444i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13176.0 | −1.93705 | −0.968527 | − | 0.248907i | \(-0.919929\pi\) | ||||
−0.968527 | + | 0.248907i | \(0.919929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000i | 0.0151820i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 6112.00i | − 0.869329i | −0.900592 | − | 0.434665i | \(-0.856867\pi\) | ||||
0.900592 | − | 0.434665i | \(-0.143133\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −810.000 | −0.114273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3312.00 | 0.463478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13618.0i | 1.89038i | 0.326515 | + | 0.945192i | \(0.394126\pi\) | ||||
−0.326515 | + | 0.945192i | \(0.605874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2340.00i | 0.319671i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −692.000 | −0.0937880 | −0.0468940 | − | 0.998900i | \(-0.514932\pi\) | ||||
−0.0468940 | + | 0.998900i | \(0.514932\pi\) | |||||||
\(380\) | 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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4068.00i | 0.534336i | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 5724.00i | 0.734701i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 8136.00i | − 0.990876i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3914.00 | −0.473190 | −0.236595 | − | 0.971608i | \(-0.576032\pi\) | ||||
−0.236595 | + | 0.971608i | \(0.576032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2862.00 | 0.343484 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5472.00i | 0.651960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7692.00i | 0.903307i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4428.00 | −0.516282 | −0.258141 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258141 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15490.0 | −1.79320 | −0.896599 | − | 0.442843i | \(-0.853970\pi\) | ||||
−0.896599 | + | 0.442843i | \(0.853970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3888.00i | − 0.446906i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3376.00i | 0.382614i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1080.00 | 0.121545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6768.00 | 0.756388 | 0.378194 | − | 0.925726i | \(-0.376545\pi\) | ||||
0.378194 | + | 0.925726i | \(0.376545\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1298.00i | − 0.144060i | −0.997402 | − | 0.0720299i | \(-0.977052\pi\) | ||||
0.997402 | − | 0.0720299i | \(-0.0229477\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(443\) | 9612.00i | 1.03088i | 0.856926 | + | 0.515440i | \(0.172372\pi\) | ||||
−0.856926 | + | 0.515440i | \(0.827628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2214.00i | − 0.234270i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −162.000 | −0.0170273 | −0.00851364 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851364 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(450\) | 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 | \(0.0223369\pi\) | ||||
−0.997539 | + | 0.0701159i | \(0.977663\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −486.000 | −0.0494217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15354.0 | −1.55121 | −0.775604 | − | 0.631220i | \(-0.782555\pi\) | ||||
−0.775604 | + | 0.631220i | \(0.782555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13024.0i | 1.30729i | 0.756800 | + | 0.653646i | \(0.226762\pi\) | ||||
−0.756800 | + | 0.653646i | \(0.773238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 14436.0i | − 1.43045i | −0.698896 | − | 0.715223i | \(-0.746325\pi\) | ||||
0.698896 | − | 0.715223i | \(-0.253675\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6056.00i | 0.563498i | 0.959488 | + | 0.281749i | \(0.0909146\pi\) | ||||
−0.959488 | + | 0.281749i | \(0.909085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2460.00 | 0.227495 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7524.00 | 0.691555 | 0.345777 | − | 0.938317i | \(-0.387615\pi\) | ||||
0.345777 | + | 0.938317i | \(0.387615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4212.00i | 0.384785i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2880.00i | − 0.259931i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5276.00 | −0.473319 | −0.236660 | − | 0.971593i | \(-0.576053\pi\) | ||||
−0.236660 | + | 0.971593i | \(0.576053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5832.00 | 0.520069 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4968.00i | − 0.440382i | −0.975457 | − | 0.220191i | \(-0.929332\pi\) | ||||
0.975457 | − | 0.220191i | \(-0.0706681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6291.00i | − 0.551071i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10998.0 | −0.957717 | −0.478858 | − | 0.877892i | \(-0.658949\pi\) | ||||
−0.478858 | + | 0.877892i | \(0.658949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 208.000 | 0.0180066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2700.00i | 0.232374i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | \(-0.621188\pi\) | ||||
−0.371593 | + | 0.928396i | \(0.621188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22436.0i | − 1.87583i | −0.346869 | − | 0.937914i | \(-0.612755\pi\) | ||||
0.346869 | − | 0.937914i | \(-0.387245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 288.000i | − 0.0238055i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6983.00 | 0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6156.00 | −0.503103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 900.000i | 0.0731395i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3348.00i | 0.269044i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10044.0 | 0.802645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4762.00 | −0.378437 | −0.189218 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189218 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3210.00i | − 0.253691i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6004.00i | − 0.469310i | −0.972079 | − | 0.234655i | \(-0.924604\pi\) | ||||
0.972079 | − | 0.234655i | \(-0.0753960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3798.00 | −0.295254 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23400.0 | 1.80921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 4096.00i | − 0.314972i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | \(-0.217912\pi\) | ||||
0.774677 | + | 0.632357i | \(0.217912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1728.00i | 0.125983i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3266.00i | 0.235642i | 0.993035 | + | 0.117821i | \(0.0375909\pi\) | ||||
−0.993035 | + | 0.117821i | \(0.962409\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4026.00 | 0.288972 | ||||||||
\(580\) | 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 | \(0.204298\pi\) | ||||
−0.801007 | + | 0.598655i | \(0.795702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1600.00 | −0.111930 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4266.00 | 0.296920 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 9522.00i | − 0.659396i | −0.944086 | − | 0.329698i | \(-0.893053\pi\) | ||||
0.944086 | − | 0.329698i | \(-0.106947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2616.00i | 0.179340i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10296.0 | 0.702309 | 0.351155 | − | 0.936318i | \(-0.385789\pi\) | ||||
0.351155 | + | 0.936318i | \(0.385789\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20656.0i | − 1.38122i | −0.723227 | − | 0.690611i | \(-0.757342\pi\) | ||||
0.723227 | − | 0.690611i | \(-0.242658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5616.00 | 0.373681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4320.00 | −0.286037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22114.0i | 1.45706i | 0.685015 | + | 0.728529i | \(0.259795\pi\) | ||||
−0.685015 | + | 0.728529i | \(0.740205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19962.0i | 1.30250i | 0.758865 | + | 0.651248i | \(0.225754\pi\) | ||||
−0.758865 | + | 0.651248i | \(0.774246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 604.000 | 0.0392194 | 0.0196097 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196097 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1944.00 | 0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5040.00i | 0.324115i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 10800.0i | − 0.687895i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4068.00 | 0.257872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 152.000 | 0.00958958 | 0.00479479 | − | 0.999989i | \(-0.498474\pi\) | ||||
0.00479479 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4020.00i | − 0.252418i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 6696.00i | − 0.406873i | −0.979088 | − | 0.203437i | \(-0.934789\pi\) | ||||
0.979088 | − | 0.203437i | \(-0.0652111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24624.0 | 1.48933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −384.000 | −0.0231185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 28422.0i | − 1.70328i | −0.524131 | − | 0.851638i | \(-0.675610\pi\) | ||||
0.524131 | − | 0.851638i | \(-0.324390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 234.000i | 0.0138953i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19908.0 | 1.17679 | 0.588396 | − | 0.808573i | \(-0.299760\pi\) | ||||
0.588396 | + | 0.808573i | \(0.299760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14318.0 | 0.842520 | 0.421260 | − | 0.906940i | \(-0.361588\pi\) | ||||
0.421260 | + | 0.906940i | \(0.361588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 540.000i | 0.0316318i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16848.0i | − 0.978047i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14640.0 | −0.846061 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15192.0 | 0.874040 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 30050.0i | − 1.72116i | −0.509313 | − | 0.860581i | \(-0.670101\pi\) | ||||
0.509313 | − | 0.860581i | \(-0.329899\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22158.0i | 1.25790i | 0.777444 | + | 0.628952i | \(0.216516\pi\) | ||||
−0.777444 | + | 0.628952i | \(0.783484\pi\) | |||||||
\(678\) | 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 | \(0.0279621\pi\) | ||||
−0.996144 | + | 0.0877325i | \(0.972038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 762.000i | 0.0423175i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4140.00 | 0.228914 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20932.0 | −1.15237 | −0.576187 | − | 0.817318i | \(-0.695460\pi\) | ||||
−0.576187 | + | 0.817318i | \(0.695460\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2592.00i | − 0.142081i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 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 | \(-0.700164\pi\) | ||||
−0.588202 | + | 0.808714i | \(0.700164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22600.0i | − 1.21248i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4464.00i | 0.237463i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12446.0 | −0.659266 | −0.329633 | − | 0.944109i | \(-0.606925\pi\) | ||||
−0.329633 | + | 0.944109i | \(0.606925\pi\) | |||||||
\(710\) | 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 | ||||||||
\(721\) | 64.0000 | 0.00330580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 15414.0i | − 0.792881i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11576.0i | 0.590550i | 0.955412 | + | 0.295275i | \(0.0954113\pi\) | ||||
−0.955412 | + | 0.295275i | \(0.904589\pi\) | |||||||
\(728\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11952.0i | 0.597364i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2540.00 | −0.126435 | −0.0632175 | − | 0.998000i | \(-0.520136\pi\) | ||||
−0.0632175 | + | 0.998000i | \(0.520136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3000.00 | 0.148728 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18792.0i | 0.927876i | 0.885868 | + | 0.463938i | \(0.153564\pi\) | ||||
−0.885868 | + | 0.463938i | \(0.846436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10692.0i | − 0.523695i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14112.0 | −0.688440 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4832.00 | 0.234783 | 0.117392 | − | 0.993086i | \(-0.462547\pi\) | ||||
0.117392 | + | 0.993086i | \(0.462547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 14364.0i | − 0.695157i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 20818.0i | − 0.999529i | −0.866161 | − | 0.499764i | \(-0.833420\pi\) | ||||
0.866161 | − | 0.499764i | \(-0.166580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7776.00 | −0.371872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12042.0 | 0.573617 | 0.286808 | − | 0.957988i | \(-0.407406\pi\) | ||||
0.286808 | + | 0.957988i | \(0.407406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12976.0i | − 0.615679i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6840.00i | 0.322005i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13058.0 | −0.612332 | −0.306166 | − | 0.951978i | \(-0.599046\pi\) | ||||
−0.306166 | + | 0.951978i | \(0.599046\pi\) | |||||||
\(770\) | 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 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 5424.00i | − 0.250431i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9000.00 | 0.413939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12960.0 | −0.593784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6318.00i | 0.288361i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 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 | ||||||||
\(791\) | −9072.00 | −0.407792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4220.00i | 0.188974i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1998.00i | − 0.0871536i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40806.0 | 1.77338 | 0.886689 | − | 0.462367i | \(-0.153000\pi\) | ||||
0.886689 | + | 0.462367i | \(0.153000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17980.0 | −0.778500 | −0.389250 | − | 0.921132i | \(-0.627266\pi\) | ||||
−0.389250 | + | 0.921132i | \(0.627266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16608.0i | 0.716443i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 45200.0i | − 1.93555i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 720.000 | 0.0307190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12834.0 | −0.545566 | −0.272783 | − | 0.962076i | \(-0.587944\pi\) | ||||
−0.272783 | + | 0.962076i | \(0.587944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37864.0i | 1.60371i | 0.597516 | + | 0.801857i | \(0.296154\pi\) | ||||
−0.597516 | + | 0.801857i | \(0.703846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | ||||||||
\(833\) | 5022.00i | 0.208886i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 432.000i | − 0.0178400i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17496.0 | −0.719939 | −0.359970 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(840\) | 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 | ||||||||
\(851\) | −16272.0 | −0.655461 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 32174.0i | − 1.29146i | −0.763565 | − | 0.645731i | \(-0.776553\pi\) | ||||
0.763565 | − | 0.645731i | \(-0.223447\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38934.0i | − 1.55188i | −0.630807 | − | 0.775939i | \(-0.717276\pi\) | ||||
0.630807 | − | 0.775939i | \(-0.282724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29780.0 | −1.18286 | −0.591432 | − | 0.806355i | \(-0.701437\pi\) | ||||
−0.591432 | + | 0.806355i | \(0.701437\pi\) | |||||||
\(860\) | 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 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 13767.0i | − 0.539275i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18432.0 | −0.719520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3320.00 | −0.129155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9486.00i | 0.367758i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32328.0i | 1.22375i | 0.790954 | + | 0.611876i | \(0.209585\pi\) | ||||
−0.790954 | + | 0.611876i | \(0.790415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4736.00 | 0.178673 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00 | 0.109640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43200.0i | 1.61885i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2160.00i | − 0.0804017i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3744.00 | −0.138898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7452.00 | 0.275541 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 10848.0i | − 0.399777i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 36316.0i | − 1.32950i | −0.747068 | − | 0.664748i | \(-0.768539\pi\) | ||||
0.747068 | − | 0.664748i | \(-0.231461\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5022.00 | −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 | ||||||||
\(913\) | 42768.0i | 1.55029i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 15264.0i | − 0.549686i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38072.0 | −1.36657 | −0.683286 | − | 0.730151i | \(-0.739450\pi\) | ||||
−0.683286 | + | 0.730151i | \(0.739450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3732.00 | 0.133522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3600.00i | − 0.128381i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 72.0000i | 0.00255101i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12798.0 | 0.451979 | 0.225990 | − | 0.974130i | \(-0.427438\pi\) | ||||
0.225990 | + | 0.974130i | \(0.427438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27900.0 | 0.982154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3672.00i | − 0.128849i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34874.0i | 1.21588i | 0.793981 | + | 0.607942i | \(0.208005\pi\) | ||||
−0.793981 | + | 0.607942i | \(0.791995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5694.00 | −0.197888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17190.0 | 0.595513 | 0.297757 | − | 0.954642i | \(-0.403762\pi\) | ||||
0.297757 | + | 0.954642i | \(0.403762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6480.00i | − 0.223773i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40284.0i | 1.38232i | 0.722703 | + | 0.691158i | \(0.242899\pi\) | ||||
−0.722703 | + | 0.691158i | \(0.757101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 260.000 | 0.00889353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27486.0 | −0.937218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15498.0i | − 0.526789i | −0.964688 | − | 0.263394i | \(-0.915158\pi\) | ||||
0.964688 | − | 0.263394i | \(-0.0848420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37160.0i | 1.23577i | 0.786270 | + | 0.617883i | \(0.212009\pi\) | ||||
−0.786270 | + | 0.617883i | \(0.787991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5400.00 | 0.179023 | ||||||||
\(970\) | 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 | \(0.0543929\pi\) | ||||
−0.985435 | + | 0.170050i | \(0.945607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22680.0 | 0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14598.0 | 0.475105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 44136.0i | − 1.43206i | −0.698067 | − | 0.716032i | \(-0.745956\pi\) | ||||
0.698067 | − | 0.716032i | \(-0.254044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10368.0i | 0.334364i | ||||||||
\(988\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39778.0i | − 1.26357i | −0.775143 | − | 0.631786i | \(-0.782322\pi\) | ||||
0.775143 | − | 0.631786i | \(-0.217678\pi\) | |||||||
\(998\) | 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 \(a_p\))