Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,4,Mod(1,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.a (trivial) |
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: | yes |
Analytic conductor: | \(69.0322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1170.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | 32.0000 | 0.877124 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 86.0000 | 1.22694 | 0.613472 | − | 0.789716i | \(-0.289772\pi\) | ||||
0.613472 | + | 0.789716i | \(0.289772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.0000 | −0.676173 | −0.338086 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338086 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −64.0000 | −0.620220 | ||||||||
\(23\) | −68.0000 | −0.616477 | −0.308239 | − | 0.951309i | \(-0.599740\pi\) | ||||
−0.308239 | + | 0.951309i | \(0.599740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −32.0000 | −0.215980 | ||||||||
\(29\) | 202.000 | 1.29346 | 0.646732 | − | 0.762717i | \(-0.276135\pi\) | ||||
0.646732 | + | 0.762717i | \(0.276135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.0000 | −0.324448 | −0.162224 | − | 0.986754i | \(-0.551867\pi\) | ||||
−0.162224 | + | 0.986754i | \(0.551867\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −172.000 | −0.867581 | ||||||||
\(35\) | −40.0000 | −0.193178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.0000 | 0.293252 | 0.146626 | − | 0.989192i | \(-0.453159\pi\) | ||||
0.146626 | + | 0.989192i | \(0.453159\pi\) | |||||||
\(38\) | 112.000 | 0.478126 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | −490.000 | −1.86647 | −0.933233 | − | 0.359271i | \(-0.883026\pi\) | ||||
−0.933233 | + | 0.359271i | \(0.883026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 460.000 | 1.63138 | 0.815690 | − | 0.578489i | \(-0.196358\pi\) | ||||
0.815690 | + | 0.578489i | \(0.196358\pi\) | |||||||
\(44\) | 128.000 | 0.438562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 136.000 | 0.435915 | ||||||||
\(47\) | 24.0000 | 0.0744843 | 0.0372421 | − | 0.999306i | \(-0.488143\pi\) | ||||
0.0372421 | + | 0.999306i | \(0.488143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | 294.000 | 0.761962 | 0.380981 | − | 0.924583i | \(-0.375586\pi\) | ||||
0.380981 | + | 0.924583i | \(0.375586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 160.000 | 0.392262 | ||||||||
\(56\) | 64.0000 | 0.152721 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −404.000 | −0.914617 | ||||||||
\(59\) | 480.000 | 1.05916 | 0.529582 | − | 0.848259i | \(-0.322349\pi\) | ||||
0.529582 | + | 0.848259i | \(0.322349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −338.000 | −0.709450 | −0.354725 | − | 0.934971i | \(-0.615426\pi\) | ||||
−0.354725 | + | 0.934971i | \(0.615426\pi\) | |||||||
\(62\) | 112.000 | 0.229420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −65.0000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 676.000 | 1.23263 | 0.616317 | − | 0.787498i | \(-0.288624\pi\) | ||||
0.616317 | + | 0.787498i | \(0.288624\pi\) | |||||||
\(68\) | 344.000 | 0.613472 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 80.0000 | 0.136598 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −210.000 | −0.336694 | −0.168347 | − | 0.985728i | \(-0.553843\pi\) | ||||
−0.168347 | + | 0.985728i | \(0.553843\pi\) | |||||||
\(74\) | −132.000 | −0.207361 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −224.000 | −0.338086 | ||||||||
\(77\) | −256.000 | −0.378882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 184.000 | 0.262046 | 0.131023 | − | 0.991379i | \(-0.458174\pi\) | ||||
0.131023 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 980.000 | 1.31979 | ||||||||
\(83\) | 660.000 | 0.872824 | 0.436412 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 430.000 | 0.548706 | ||||||||
\(86\) | −920.000 | −1.15356 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −256.000 | −0.310110 | ||||||||
\(89\) | 286.000 | 0.340629 | 0.170314 | − | 0.985390i | \(-0.445522\pi\) | ||||
0.170314 | + | 0.985390i | \(0.445522\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 104.000 | 0.119804 | ||||||||
\(92\) | −272.000 | −0.308239 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −48.0000 | −0.0526683 | ||||||||
\(95\) | −280.000 | −0.302394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1202.00 | −1.25819 | −0.629096 | − | 0.777328i | \(-0.716575\pi\) | ||||
−0.629096 | + | 0.777328i | \(0.716575\pi\) | |||||||
\(98\) | 558.000 | 0.575168 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1066.00 | 1.05021 | 0.525104 | − | 0.851038i | \(-0.324026\pi\) | ||||
0.525104 | + | 0.851038i | \(0.324026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 556.000 | 0.531886 | 0.265943 | − | 0.963989i | \(-0.414317\pi\) | ||||
0.265943 | + | 0.963989i | \(0.414317\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −588.000 | −0.538789 | ||||||||
\(107\) | −412.000 | −0.372239 | −0.186119 | − | 0.982527i | \(-0.559591\pi\) | ||||
−0.186119 | + | 0.982527i | \(0.559591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1814.00 | −1.59403 | −0.797017 | − | 0.603957i | \(-0.793590\pi\) | ||||
−0.797017 | + | 0.603957i | \(0.793590\pi\) | |||||||
\(110\) | −320.000 | −0.277371 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −128.000 | −0.107990 | ||||||||
\(113\) | 454.000 | 0.377953 | 0.188977 | − | 0.981982i | \(-0.439483\pi\) | ||||
0.188977 | + | 0.981982i | \(0.439483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −340.000 | −0.275697 | ||||||||
\(116\) | 808.000 | 0.646732 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −960.000 | −0.748942 | ||||||||
\(119\) | −688.000 | −0.529990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | 676.000 | 0.501657 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −224.000 | −0.162224 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −508.000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 130.000 | 0.0877058 | ||||||||
\(131\) | 1876.00 | 1.25120 | 0.625599 | − | 0.780145i | \(-0.284855\pi\) | ||||
0.625599 | + | 0.780145i | \(0.284855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 448.000 | 0.292079 | ||||||||
\(134\) | −1352.00 | −0.871605 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −688.000 | −0.433791 | ||||||||
\(137\) | −574.000 | −0.357957 | −0.178979 | − | 0.983853i | \(-0.557279\pi\) | ||||
−0.178979 | + | 0.983853i | \(0.557279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1852.00 | −1.13010 | −0.565052 | − | 0.825055i | \(-0.691144\pi\) | ||||
−0.565052 | + | 0.825055i | \(0.691144\pi\) | |||||||
\(140\) | −160.000 | −0.0965891 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 240.000 | 0.141833 | ||||||||
\(143\) | −416.000 | −0.243270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1010.00 | 0.578455 | ||||||||
\(146\) | 420.000 | 0.238078 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 264.000 | 0.146626 | ||||||||
\(149\) | 2902.00 | 1.59558 | 0.797789 | − | 0.602937i | \(-0.206003\pi\) | ||||
0.797789 | + | 0.602937i | \(0.206003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1736.00 | 0.935587 | 0.467794 | − | 0.883838i | \(-0.345049\pi\) | ||||
0.467794 | + | 0.883838i | \(0.345049\pi\) | |||||||
\(152\) | 448.000 | 0.239063 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 512.000 | 0.267910 | ||||||||
\(155\) | −280.000 | −0.145098 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3770.00 | 1.91643 | 0.958213 | − | 0.286057i | \(-0.0923447\pi\) | ||||
0.958213 | + | 0.286057i | \(0.0923447\pi\) | |||||||
\(158\) | −368.000 | −0.185294 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 544.000 | 0.266293 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2028.00 | 0.974511 | 0.487255 | − | 0.873260i | \(-0.337998\pi\) | ||||
0.487255 | + | 0.873260i | \(0.337998\pi\) | |||||||
\(164\) | −1960.00 | −0.933233 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1320.00 | −0.617180 | ||||||||
\(167\) | 240.000 | 0.111208 | 0.0556041 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556041 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −860.000 | −0.387994 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1840.00 | 0.815690 | ||||||||
\(173\) | 1630.00 | 0.716339 | 0.358169 | − | 0.933657i | \(-0.383401\pi\) | ||||
0.358169 | + | 0.933657i | \(0.383401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −200.000 | −0.0863919 | ||||||||
\(176\) | 512.000 | 0.219281 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −572.000 | −0.240861 | ||||||||
\(179\) | −764.000 | −0.319017 | −0.159508 | − | 0.987197i | \(-0.550991\pi\) | ||||
−0.159508 | + | 0.987197i | \(0.550991\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1790.00 | 0.735081 | 0.367540 | − | 0.930008i | \(-0.380200\pi\) | ||||
0.367540 | + | 0.930008i | \(0.380200\pi\) | |||||||
\(182\) | −208.000 | −0.0847142 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 544.000 | 0.217958 | ||||||||
\(185\) | 330.000 | 0.131146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2752.00 | 1.07618 | ||||||||
\(188\) | 96.0000 | 0.0372421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 560.000 | 0.213825 | ||||||||
\(191\) | −2440.00 | −0.924357 | −0.462179 | − | 0.886787i | \(-0.652932\pi\) | ||||
−0.462179 | + | 0.886787i | \(0.652932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3102.00 | 1.15693 | 0.578463 | − | 0.815708i | \(-0.303653\pi\) | ||||
0.578463 | + | 0.815708i | \(0.303653\pi\) | |||||||
\(194\) | 2404.00 | 0.889676 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1116.00 | −0.406706 | ||||||||
\(197\) | 1982.00 | 0.716810 | 0.358405 | − | 0.933566i | \(-0.383321\pi\) | ||||
0.358405 | + | 0.933566i | \(0.383321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2520.00 | −0.897679 | −0.448839 | − | 0.893612i | \(-0.648162\pi\) | ||||
−0.448839 | + | 0.893612i | \(0.648162\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2132.00 | −0.742609 | ||||||||
\(203\) | −1616.00 | −0.558724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2450.00 | −0.834709 | ||||||||
\(206\) | −1112.00 | −0.376101 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −1792.00 | −0.593087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3188.00 | 1.04015 | 0.520073 | − | 0.854122i | \(-0.325905\pi\) | ||||
0.520073 | + | 0.854122i | \(0.325905\pi\) | |||||||
\(212\) | 1176.00 | 0.380981 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 824.000 | 0.263213 | ||||||||
\(215\) | 2300.00 | 0.729575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 448.000 | 0.140148 | ||||||||
\(218\) | 3628.00 | 1.12715 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 640.000 | 0.196131 | ||||||||
\(221\) | −1118.00 | −0.340293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6392.00 | 1.91946 | 0.959731 | − | 0.280921i | \(-0.0906399\pi\) | ||||
0.959731 | + | 0.280921i | \(0.0906399\pi\) | |||||||
\(224\) | 256.000 | 0.0763604 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −908.000 | −0.267253 | ||||||||
\(227\) | 5748.00 | 1.68065 | 0.840326 | − | 0.542081i | \(-0.182363\pi\) | ||||
0.840326 | + | 0.542081i | \(0.182363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2410.00 | 0.695447 | 0.347723 | − | 0.937597i | \(-0.386955\pi\) | ||||
0.347723 | + | 0.937597i | \(0.386955\pi\) | |||||||
\(230\) | 680.000 | 0.194947 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1616.00 | −0.457309 | ||||||||
\(233\) | 1358.00 | 0.381826 | 0.190913 | − | 0.981607i | \(-0.438855\pi\) | ||||
0.190913 | + | 0.981607i | \(0.438855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 120.000 | 0.0333104 | ||||||||
\(236\) | 1920.00 | 0.529582 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1376.00 | 0.374760 | ||||||||
\(239\) | −3256.00 | −0.881226 | −0.440613 | − | 0.897697i | \(-0.645239\pi\) | ||||
−0.440613 | + | 0.897697i | \(0.645239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4898.00 | 1.30916 | 0.654581 | − | 0.755992i | \(-0.272845\pi\) | ||||
0.654581 | + | 0.755992i | \(0.272845\pi\) | |||||||
\(242\) | 614.000 | 0.163097 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1352.00 | −0.354725 | ||||||||
\(245\) | −1395.00 | −0.363768 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 728.000 | 0.187537 | ||||||||
\(248\) | 448.000 | 0.114710 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 4100.00 | 1.03103 | 0.515517 | − | 0.856879i | \(-0.327600\pi\) | ||||
0.515517 | + | 0.856879i | \(0.327600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2176.00 | −0.540727 | ||||||||
\(254\) | 1016.00 | 0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5270.00 | 1.27912 | 0.639559 | − | 0.768742i | \(-0.279117\pi\) | ||||
0.639559 | + | 0.768742i | \(0.279117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −528.000 | −0.126673 | ||||||||
\(260\) | −260.000 | −0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3752.00 | −0.884730 | ||||||||
\(263\) | 84.0000 | 0.0196945 | 0.00984727 | − | 0.999952i | \(-0.496865\pi\) | ||||
0.00984727 | + | 0.999952i | \(0.496865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1470.00 | 0.340760 | ||||||||
\(266\) | −896.000 | −0.206531 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2704.00 | 0.616317 | ||||||||
\(269\) | 7186.00 | 1.62877 | 0.814383 | − | 0.580328i | \(-0.197075\pi\) | ||||
0.814383 | + | 0.580328i | \(0.197075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6368.00 | 1.42741 | 0.713706 | − | 0.700446i | \(-0.247015\pi\) | ||||
0.713706 | + | 0.700446i | \(0.247015\pi\) | |||||||
\(272\) | 1376.00 | 0.306736 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1148.00 | 0.253114 | ||||||||
\(275\) | 800.000 | 0.175425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5846.00 | −1.26806 | −0.634029 | − | 0.773309i | \(-0.718600\pi\) | ||||
−0.634029 | + | 0.773309i | \(0.718600\pi\) | |||||||
\(278\) | 3704.00 | 0.799105 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 320.000 | 0.0682988 | ||||||||
\(281\) | −4274.00 | −0.907350 | −0.453675 | − | 0.891167i | \(-0.649887\pi\) | ||||
−0.453675 | + | 0.891167i | \(0.649887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 532.000 | 0.111746 | 0.0558730 | − | 0.998438i | \(-0.482206\pi\) | ||||
0.0558730 | + | 0.998438i | \(0.482206\pi\) | |||||||
\(284\) | −480.000 | −0.100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 832.000 | 0.172018 | ||||||||
\(287\) | 3920.00 | 0.806238 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2483.00 | 0.505394 | ||||||||
\(290\) | −2020.00 | −0.409029 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −840.000 | −0.168347 | ||||||||
\(293\) | 1374.00 | 0.273959 | 0.136979 | − | 0.990574i | \(-0.456261\pi\) | ||||
0.136979 | + | 0.990574i | \(0.456261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2400.00 | 0.473673 | ||||||||
\(296\) | −528.000 | −0.103680 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5804.00 | −1.12824 | ||||||||
\(299\) | 884.000 | 0.170980 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3680.00 | −0.704690 | ||||||||
\(302\) | −3472.00 | −0.661560 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −896.000 | −0.169043 | ||||||||
\(305\) | −1690.00 | −0.317276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8532.00 | −1.58615 | −0.793073 | − | 0.609126i | \(-0.791520\pi\) | ||||
−0.793073 | + | 0.609126i | \(0.791520\pi\) | |||||||
\(308\) | −1024.00 | −0.189441 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 560.000 | 0.102600 | ||||||||
\(311\) | 10672.0 | 1.94583 | 0.972916 | − | 0.231160i | \(-0.0742521\pi\) | ||||
0.972916 | + | 0.231160i | \(0.0742521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7318.00 | −1.32153 | −0.660763 | − | 0.750594i | \(-0.729767\pi\) | ||||
−0.660763 | + | 0.750594i | \(0.729767\pi\) | |||||||
\(314\) | −7540.00 | −1.35512 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 736.000 | 0.131023 | ||||||||
\(317\) | −5674.00 | −1.00531 | −0.502656 | − | 0.864487i | \(-0.667644\pi\) | ||||
−0.502656 | + | 0.864487i | \(0.667644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6464.00 | 1.13453 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1088.00 | −0.188298 | ||||||||
\(323\) | −4816.00 | −0.829627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −325.000 | −0.0554700 | ||||||||
\(326\) | −4056.00 | −0.689083 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3920.00 | 0.659896 | ||||||||
\(329\) | −192.000 | −0.0321742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3664.00 | −0.608434 | −0.304217 | − | 0.952603i | \(-0.598395\pi\) | ||||
−0.304217 | + | 0.952603i | \(0.598395\pi\) | |||||||
\(332\) | 2640.00 | 0.436412 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −480.000 | −0.0786360 | ||||||||
\(335\) | 3380.00 | 0.551251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −494.000 | −0.0798513 | −0.0399257 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399257 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1720.00 | 0.274353 | ||||||||
\(341\) | −1792.00 | −0.284581 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | −3680.00 | −0.576780 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3260.00 | −0.506528 | ||||||||
\(347\) | 7988.00 | 1.23579 | 0.617894 | − | 0.786262i | \(-0.287986\pi\) | ||||
0.617894 | + | 0.786262i | \(0.287986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2138.00 | 0.327921 | 0.163961 | − | 0.986467i | \(-0.447573\pi\) | ||||
0.163961 | + | 0.986467i | \(0.447573\pi\) | |||||||
\(350\) | 400.000 | 0.0610883 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1024.00 | −0.155055 | ||||||||
\(353\) | −3582.00 | −0.540087 | −0.270043 | − | 0.962848i | \(-0.587038\pi\) | ||||
−0.270043 | + | 0.962848i | \(0.587038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −600.000 | −0.0897034 | ||||||||
\(356\) | 1144.00 | 0.170314 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1528.00 | 0.225579 | ||||||||
\(359\) | −9456.00 | −1.39016 | −0.695082 | − | 0.718931i | \(-0.744632\pi\) | ||||
−0.695082 | + | 0.718931i | \(0.744632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3723.00 | −0.542790 | ||||||||
\(362\) | −3580.00 | −0.519781 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 416.000 | 0.0599020 | ||||||||
\(365\) | −1050.00 | −0.150574 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1220.00 | 0.173524 | 0.0867622 | − | 0.996229i | \(-0.472348\pi\) | ||||
0.0867622 | + | 0.996229i | \(0.472348\pi\) | |||||||
\(368\) | −1088.00 | −0.154119 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −660.000 | −0.0927345 | ||||||||
\(371\) | −2352.00 | −0.329137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7778.00 | 1.07970 | 0.539852 | − | 0.841760i | \(-0.318480\pi\) | ||||
0.539852 | + | 0.841760i | \(0.318480\pi\) | |||||||
\(374\) | −5504.00 | −0.760976 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −192.000 | −0.0263342 | ||||||||
\(377\) | −2626.00 | −0.358742 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1856.00 | −0.251547 | −0.125774 | − | 0.992059i | \(-0.540141\pi\) | ||||
−0.125774 | + | 0.992059i | \(0.540141\pi\) | |||||||
\(380\) | −1120.00 | −0.151197 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4880.00 | 0.653619 | ||||||||
\(383\) | 8624.00 | 1.15056 | 0.575282 | − | 0.817955i | \(-0.304892\pi\) | ||||
0.575282 | + | 0.817955i | \(0.304892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1280.00 | −0.169441 | ||||||||
\(386\) | −6204.00 | −0.818071 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4808.00 | −0.629096 | ||||||||
\(389\) | −350.000 | −0.0456188 | −0.0228094 | − | 0.999740i | \(-0.507261\pi\) | ||||
−0.0228094 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5848.00 | −0.756384 | ||||||||
\(392\) | 2232.00 | 0.287584 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3964.00 | −0.506862 | ||||||||
\(395\) | 920.000 | 0.117190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5334.00 | −0.674322 | −0.337161 | − | 0.941447i | \(-0.609467\pi\) | ||||
−0.337161 | + | 0.941447i | \(0.609467\pi\) | |||||||
\(398\) | 5040.00 | 0.634755 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −10554.0 | −1.31432 | −0.657159 | − | 0.753752i | \(-0.728242\pi\) | ||||
−0.657159 | + | 0.753752i | \(0.728242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 728.000 | 0.0899858 | ||||||||
\(404\) | 4264.00 | 0.525104 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3232.00 | 0.395078 | ||||||||
\(407\) | 2112.00 | 0.257219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2814.00 | −0.340204 | −0.170102 | − | 0.985426i | \(-0.554410\pi\) | ||||
−0.170102 | + | 0.985426i | \(0.554410\pi\) | |||||||
\(410\) | 4900.00 | 0.590229 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2224.00 | 0.265943 | ||||||||
\(413\) | −3840.00 | −0.457516 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3300.00 | 0.390339 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3584.00 | 0.419376 | ||||||||
\(419\) | −764.000 | −0.0890784 | −0.0445392 | − | 0.999008i | \(-0.514182\pi\) | ||||
−0.0445392 | + | 0.999008i | \(0.514182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5330.00 | 0.617027 | 0.308513 | − | 0.951220i | \(-0.400169\pi\) | ||||
0.308513 | + | 0.951220i | \(0.400169\pi\) | |||||||
\(422\) | −6376.00 | −0.735495 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2352.00 | −0.269394 | ||||||||
\(425\) | 2150.00 | 0.245389 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2704.00 | 0.306454 | ||||||||
\(428\) | −1648.00 | −0.186119 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4600.00 | −0.515888 | ||||||||
\(431\) | 11072.0 | 1.23740 | 0.618700 | − | 0.785627i | \(-0.287660\pi\) | ||||
0.618700 | + | 0.785627i | \(0.287660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7426.00 | 0.824182 | 0.412091 | − | 0.911143i | \(-0.364799\pi\) | ||||
0.412091 | + | 0.911143i | \(0.364799\pi\) | |||||||
\(434\) | −896.000 | −0.0990999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7256.00 | −0.797017 | ||||||||
\(437\) | 3808.00 | 0.416845 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3392.00 | 0.368773 | 0.184386 | − | 0.982854i | \(-0.440970\pi\) | ||||
0.184386 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(440\) | −1280.00 | −0.138685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2236.00 | 0.240624 | ||||||||
\(443\) | 13972.0 | 1.49849 | 0.749244 | − | 0.662295i | \(-0.230417\pi\) | ||||
0.749244 | + | 0.662295i | \(0.230417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1430.00 | 0.152334 | ||||||||
\(446\) | −12784.0 | −1.35726 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −512.000 | −0.0539949 | ||||||||
\(449\) | −16986.0 | −1.78534 | −0.892671 | − | 0.450708i | \(-0.851172\pi\) | ||||
−0.892671 | + | 0.450708i | \(0.851172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15680.0 | −1.63712 | ||||||||
\(452\) | 1816.00 | 0.188977 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11496.0 | −1.18840 | ||||||||
\(455\) | 520.000 | 0.0535780 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1910.00 | 0.195506 | 0.0977528 | − | 0.995211i | \(-0.468835\pi\) | ||||
0.0977528 | + | 0.995211i | \(0.468835\pi\) | |||||||
\(458\) | −4820.00 | −0.491755 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1360.00 | −0.137849 | ||||||||
\(461\) | −9834.00 | −0.993525 | −0.496763 | − | 0.867887i | \(-0.665478\pi\) | ||||
−0.496763 | + | 0.867887i | \(0.665478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13072.0 | −1.31211 | −0.656055 | − | 0.754713i | \(-0.727776\pi\) | ||||
−0.656055 | + | 0.754713i | \(0.727776\pi\) | |||||||
\(464\) | 3232.00 | 0.323366 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2716.00 | −0.269992 | ||||||||
\(467\) | −19860.0 | −1.96790 | −0.983952 | − | 0.178433i | \(-0.942897\pi\) | ||||
−0.983952 | + | 0.178433i | \(0.942897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5408.00 | −0.532448 | ||||||||
\(470\) | −240.000 | −0.0235540 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3840.00 | −0.374471 | ||||||||
\(473\) | 14720.0 | 1.43092 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1400.00 | −0.135235 | ||||||||
\(476\) | −2752.00 | −0.264995 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6512.00 | 0.623121 | ||||||||
\(479\) | 3672.00 | 0.350267 | 0.175134 | − | 0.984545i | \(-0.443964\pi\) | ||||
0.175134 | + | 0.984545i | \(0.443964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −858.000 | −0.0813335 | ||||||||
\(482\) | −9796.00 | −0.925717 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1228.00 | −0.115327 | ||||||||
\(485\) | −6010.00 | −0.562680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3488.00 | 0.324551 | 0.162276 | − | 0.986745i | \(-0.448117\pi\) | ||||
0.162276 | + | 0.986745i | \(0.448117\pi\) | |||||||
\(488\) | 2704.00 | 0.250829 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2790.00 | 0.257223 | ||||||||
\(491\) | 5260.00 | 0.483463 | 0.241732 | − | 0.970343i | \(-0.422285\pi\) | ||||
0.241732 | + | 0.970343i | \(0.422285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17372.0 | 1.58701 | ||||||||
\(494\) | −1456.00 | −0.132608 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −896.000 | −0.0811121 | ||||||||
\(497\) | 960.000 | 0.0866436 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8048.00 | −0.722000 | −0.361000 | − | 0.932566i | \(-0.617565\pi\) | ||||
−0.361000 | + | 0.932566i | \(0.617565\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8200.00 | −0.729052 | ||||||||
\(503\) | 732.000 | 0.0648872 | 0.0324436 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324436 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5330.00 | 0.469667 | ||||||||
\(506\) | 4352.00 | 0.382352 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2032.00 | −0.177471 | ||||||||
\(509\) | −13826.0 | −1.20398 | −0.601991 | − | 0.798503i | \(-0.705626\pi\) | ||||
−0.601991 | + | 0.798503i | \(0.705626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1680.00 | 0.145438 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10540.0 | −0.904474 | ||||||||
\(515\) | 2780.00 | 0.237867 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 768.000 | 0.0653319 | ||||||||
\(518\) | 1056.00 | 0.0895714 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 520.000 | 0.0438529 | ||||||||
\(521\) | 1926.00 | 0.161957 | 0.0809785 | − | 0.996716i | \(-0.474195\pi\) | ||||
0.0809785 | + | 0.996716i | \(0.474195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4892.00 | 0.409010 | 0.204505 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204505 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(524\) | 7504.00 | 0.625599 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −168.000 | −0.0139261 | ||||||||
\(527\) | −4816.00 | −0.398080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7543.00 | −0.619956 | ||||||||
\(530\) | −2940.00 | −0.240954 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1792.00 | 0.146040 | ||||||||
\(533\) | 6370.00 | 0.517665 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2060.00 | −0.166470 | ||||||||
\(536\) | −5408.00 | −0.435802 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14372.0 | −1.15171 | ||||||||
\(539\) | −8928.00 | −0.713462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15042.0 | 1.19539 | 0.597695 | − | 0.801724i | \(-0.296083\pi\) | ||||
0.597695 | + | 0.801724i | \(0.296083\pi\) | |||||||
\(542\) | −12736.0 | −1.00933 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2752.00 | −0.216895 | ||||||||
\(545\) | −9070.00 | −0.712874 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −996.000 | −0.0778535 | −0.0389268 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389268 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(548\) | −2296.00 | −0.178979 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1600.00 | −0.124044 | ||||||||
\(551\) | −11312.0 | −0.874605 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1472.00 | −0.113193 | ||||||||
\(554\) | 11692.0 | 0.896652 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7408.00 | −0.565052 | ||||||||
\(557\) | −15626.0 | −1.18868 | −0.594340 | − | 0.804214i | \(-0.702587\pi\) | ||||
−0.594340 | + | 0.804214i | \(0.702587\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5980.00 | −0.452463 | ||||||||
\(560\) | −640.000 | −0.0482945 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8548.00 | 0.641594 | ||||||||
\(563\) | 20892.0 | 1.56393 | 0.781965 | − | 0.623322i | \(-0.214217\pi\) | ||||
0.781965 | + | 0.623322i | \(0.214217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2270.00 | 0.169026 | ||||||||
\(566\) | −1064.00 | −0.0790164 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 960.000 | 0.0709167 | ||||||||
\(569\) | −1994.00 | −0.146912 | −0.0734559 | − | 0.997298i | \(-0.523403\pi\) | ||||
−0.0734559 | + | 0.997298i | \(0.523403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24292.0 | −1.78037 | −0.890183 | − | 0.455604i | \(-0.849423\pi\) | ||||
−0.890183 | + | 0.455604i | \(0.849423\pi\) | |||||||
\(572\) | −1664.00 | −0.121635 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7840.00 | −0.570096 | ||||||||
\(575\) | −1700.00 | −0.123295 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17914.0 | −1.29249 | −0.646247 | − | 0.763128i | \(-0.723663\pi\) | ||||
−0.646247 | + | 0.763128i | \(0.723663\pi\) | |||||||
\(578\) | −4966.00 | −0.357367 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4040.00 | 0.289227 | ||||||||
\(581\) | −5280.00 | −0.377025 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9408.00 | 0.668335 | ||||||||
\(584\) | 1680.00 | 0.119039 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2748.00 | −0.193718 | ||||||||
\(587\) | 996.000 | 0.0700329 | 0.0350165 | − | 0.999387i | \(-0.488852\pi\) | ||||
0.0350165 | + | 0.999387i | \(0.488852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3136.00 | 0.219383 | ||||||||
\(590\) | −4800.00 | −0.334937 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1056.00 | 0.0733131 | ||||||||
\(593\) | −20014.0 | −1.38596 | −0.692982 | − | 0.720955i | \(-0.743703\pi\) | ||||
−0.692982 | + | 0.720955i | \(0.743703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3440.00 | −0.237019 | ||||||||
\(596\) | 11608.0 | 0.797789 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1768.00 | −0.120901 | ||||||||
\(599\) | −12312.0 | −0.839824 | −0.419912 | − | 0.907565i | \(-0.637939\pi\) | ||||
−0.419912 | + | 0.907565i | \(0.637939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19110.0 | −1.29703 | −0.648513 | − | 0.761203i | \(-0.724609\pi\) | ||||
−0.648513 | + | 0.761203i | \(0.724609\pi\) | |||||||
\(602\) | 7360.00 | 0.498291 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6944.00 | 0.467794 | ||||||||
\(605\) | −1535.00 | −0.103151 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25452.0 | 1.70192 | 0.850959 | − | 0.525231i | \(-0.176021\pi\) | ||||
0.850959 | + | 0.525231i | \(0.176021\pi\) | |||||||
\(608\) | 1792.00 | 0.119532 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3380.00 | 0.224348 | ||||||||
\(611\) | −312.000 | −0.0206582 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4142.00 | −0.272910 | −0.136455 | − | 0.990646i | \(-0.543571\pi\) | ||||
−0.136455 | + | 0.990646i | \(0.543571\pi\) | |||||||
\(614\) | 17064.0 | 1.12157 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2048.00 | 0.133955 | ||||||||
\(617\) | −1382.00 | −0.0901738 | −0.0450869 | − | 0.998983i | \(-0.514356\pi\) | ||||
−0.0450869 | + | 0.998983i | \(0.514356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5456.00 | 0.354273 | 0.177137 | − | 0.984186i | \(-0.443317\pi\) | ||||
0.177137 | + | 0.984186i | \(0.443317\pi\) | |||||||
\(620\) | −1120.00 | −0.0725488 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21344.0 | −1.37591 | ||||||||
\(623\) | −2288.00 | −0.147138 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 14636.0 | 0.934460 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15080.0 | 0.958213 | ||||||||
\(629\) | 5676.00 | 0.359804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13960.0 | 0.880727 | 0.440364 | − | 0.897820i | \(-0.354850\pi\) | ||||
0.440364 | + | 0.897820i | \(0.354850\pi\) | |||||||
\(632\) | −1472.00 | −0.0926472 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11348.0 | 0.710862 | ||||||||
\(635\) | −2540.00 | −0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3627.00 | 0.225600 | ||||||||
\(638\) | −12928.0 | −0.802233 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −9138.00 | −0.563072 | −0.281536 | − | 0.959551i | \(-0.590844\pi\) | ||||
−0.281536 | + | 0.959551i | \(0.590844\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20852.0 | 1.27888 | 0.639442 | − | 0.768839i | \(-0.279165\pi\) | ||||
0.639442 | + | 0.768839i | \(0.279165\pi\) | |||||||
\(644\) | 2176.00 | 0.133147 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9632.00 | 0.586635 | ||||||||
\(647\) | −25524.0 | −1.55093 | −0.775465 | − | 0.631390i | \(-0.782485\pi\) | ||||
−0.775465 | + | 0.631390i | \(0.782485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15360.0 | 0.929018 | ||||||||
\(650\) | 650.000 | 0.0392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8112.00 | 0.487255 | ||||||||
\(653\) | 30518.0 | 1.82888 | 0.914442 | − | 0.404716i | \(-0.132630\pi\) | ||||
0.914442 | + | 0.404716i | \(0.132630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9380.00 | 0.559553 | ||||||||
\(656\) | −7840.00 | −0.466617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 384.000 | 0.0227506 | ||||||||
\(659\) | −30012.0 | −1.77405 | −0.887027 | − | 0.461718i | \(-0.847233\pi\) | ||||
−0.887027 | + | 0.461718i | \(0.847233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1610.00 | 0.0947379 | 0.0473689 | − | 0.998877i | \(-0.484916\pi\) | ||||
0.0473689 | + | 0.998877i | \(0.484916\pi\) | |||||||
\(662\) | 7328.00 | 0.430228 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5280.00 | −0.308590 | ||||||||
\(665\) | 2240.00 | 0.130622 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13736.0 | −0.797391 | ||||||||
\(668\) | 960.000 | 0.0556041 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6760.00 | −0.389793 | ||||||||
\(671\) | −10816.0 | −0.622276 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17066.0 | 0.977483 | 0.488741 | − | 0.872429i | \(-0.337456\pi\) | ||||
0.488741 | + | 0.872429i | \(0.337456\pi\) | |||||||
\(674\) | 988.000 | 0.0564634 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | −27698.0 | −1.57241 | −0.786204 | − | 0.617967i | \(-0.787957\pi\) | ||||
−0.786204 | + | 0.617967i | \(0.787957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9616.00 | 0.543488 | ||||||||
\(680\) | −3440.00 | −0.193997 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3584.00 | 0.201229 | ||||||||
\(683\) | 25932.0 | 1.45280 | 0.726399 | − | 0.687274i | \(-0.241193\pi\) | ||||
0.726399 | + | 0.687274i | \(0.241193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2870.00 | −0.160083 | ||||||||
\(686\) | −9952.00 | −0.553891 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7360.00 | 0.407845 | ||||||||
\(689\) | −3822.00 | −0.211330 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19848.0 | −1.09270 | −0.546348 | − | 0.837558i | \(-0.683983\pi\) | ||||
−0.546348 | + | 0.837558i | \(0.683983\pi\) | |||||||
\(692\) | 6520.00 | 0.358169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15976.0 | −0.873834 | ||||||||
\(695\) | −9260.00 | −0.505398 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42140.0 | −2.29005 | ||||||||
\(698\) | −4276.00 | −0.231875 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −800.000 | −0.0431959 | ||||||||
\(701\) | −29758.0 | −1.60334 | −0.801672 | − | 0.597764i | \(-0.796056\pi\) | ||||
−0.801672 | + | 0.597764i | \(0.796056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3696.00 | −0.198289 | ||||||||
\(704\) | 2048.00 | 0.109640 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7164.00 | 0.381899 | ||||||||
\(707\) | −8528.00 | −0.453647 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23722.0 | 1.25656 | 0.628278 | − | 0.777989i | \(-0.283760\pi\) | ||||
0.628278 | + | 0.777989i | \(0.283760\pi\) | |||||||
\(710\) | 1200.00 | 0.0634299 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2288.00 | −0.120430 | ||||||||
\(713\) | 3808.00 | 0.200015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2080.00 | −0.108794 | ||||||||
\(716\) | −3056.00 | −0.159508 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18912.0 | 0.982994 | ||||||||
\(719\) | 18168.0 | 0.942353 | 0.471177 | − | 0.882039i | \(-0.343829\pi\) | ||||
0.471177 | + | 0.882039i | \(0.343829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4448.00 | −0.229753 | ||||||||
\(722\) | 7446.00 | 0.383811 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7160.00 | 0.367540 | ||||||||
\(725\) | 5050.00 | 0.258693 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10708.0 | −0.546269 | −0.273135 | − | 0.961976i | \(-0.588060\pi\) | ||||
−0.273135 | + | 0.961976i | \(0.588060\pi\) | |||||||
\(728\) | −832.000 | −0.0423571 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2100.00 | 0.106472 | ||||||||
\(731\) | 39560.0 | 2.00161 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27894.0 | −1.40558 | −0.702789 | − | 0.711399i | \(-0.748062\pi\) | ||||
−0.702789 | + | 0.711399i | \(0.748062\pi\) | |||||||
\(734\) | −2440.00 | −0.122700 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2176.00 | 0.108979 | ||||||||
\(737\) | 21632.0 | 1.08117 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26512.0 | −1.31970 | −0.659851 | − | 0.751397i | \(-0.729381\pi\) | ||||
−0.659851 | + | 0.751397i | \(0.729381\pi\) | |||||||
\(740\) | 1320.00 | 0.0655732 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4704.00 | 0.232735 | ||||||||
\(743\) | −24024.0 | −1.18621 | −0.593106 | − | 0.805125i | \(-0.702098\pi\) | ||||
−0.593106 | + | 0.805125i | \(0.702098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14510.0 | 0.713564 | ||||||||
\(746\) | −15556.0 | −0.763466 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11008.0 | 0.538091 | ||||||||
\(749\) | 3296.00 | 0.160792 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16976.0 | −0.824851 | −0.412425 | − | 0.910991i | \(-0.635318\pi\) | ||||
−0.412425 | + | 0.910991i | \(0.635318\pi\) | |||||||
\(752\) | 384.000 | 0.0186211 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5252.00 | 0.253669 | ||||||||
\(755\) | 8680.00 | 0.418407 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23894.0 | −1.14722 | −0.573608 | − | 0.819130i | \(-0.694457\pi\) | ||||
−0.573608 | + | 0.819130i | \(0.694457\pi\) | |||||||
\(758\) | 3712.00 | 0.177871 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2240.00 | 0.106912 | ||||||||
\(761\) | 14254.0 | 0.678984 | 0.339492 | − | 0.940609i | \(-0.389745\pi\) | ||||
0.339492 | + | 0.940609i | \(0.389745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14512.0 | 0.688558 | ||||||||
\(764\) | −9760.00 | −0.462179 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17248.0 | −0.813571 | ||||||||
\(767\) | −6240.00 | −0.293759 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40670.0 | −1.90715 | −0.953575 | − | 0.301157i | \(-0.902627\pi\) | ||||
−0.953575 | + | 0.301157i | \(0.902627\pi\) | |||||||
\(770\) | 2560.00 | 0.119813 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12408.0 | 0.578463 | ||||||||
\(773\) | 7102.00 | 0.330454 | 0.165227 | − | 0.986256i | \(-0.447164\pi\) | ||||
0.165227 | + | 0.986256i | \(0.447164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1400.00 | −0.0648897 | ||||||||
\(776\) | 9616.00 | 0.444838 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 700.000 | 0.0322573 | ||||||||
\(779\) | 27440.0 | 1.26205 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3840.00 | −0.175936 | ||||||||
\(782\) | 11696.0 | 0.534844 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4464.00 | −0.203353 | ||||||||
\(785\) | 18850.0 | 0.857051 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29564.0 | 1.33906 | 0.669532 | − | 0.742784i | \(-0.266495\pi\) | ||||
0.669532 | + | 0.742784i | \(0.266495\pi\) | |||||||
\(788\) | 7928.00 | 0.358405 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1840.00 | −0.0828662 | ||||||||
\(791\) | −3632.00 | −0.163260 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4394.00 | 0.196766 | ||||||||
\(794\) | 10668.0 | 0.476818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10080.0 | −0.448839 | ||||||||
\(797\) | 44814.0 | 1.99171 | 0.995855 | − | 0.0909519i | \(-0.0289910\pi\) | ||||
0.995855 | + | 0.0909519i | \(0.0289910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2064.00 | 0.0913881 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21108.0 | 0.929363 | ||||||||
\(803\) | −6720.00 | −0.295322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2720.00 | 0.119090 | ||||||||
\(806\) | −1456.00 | −0.0636295 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8528.00 | −0.371304 | ||||||||
\(809\) | 34326.0 | 1.49177 | 0.745883 | − | 0.666078i | \(-0.232028\pi\) | ||||
0.745883 | + | 0.666078i | \(0.232028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13768.0 | −0.596128 | −0.298064 | − | 0.954546i | \(-0.596341\pi\) | ||||
−0.298064 | + | 0.954546i | \(0.596341\pi\) | |||||||
\(812\) | −6464.00 | −0.279362 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4224.00 | −0.181881 | ||||||||
\(815\) | 10140.0 | 0.435814 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25760.0 | −1.10309 | ||||||||
\(818\) | 5628.00 | 0.240560 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9800.00 | −0.417355 | ||||||||
\(821\) | 41550.0 | 1.76627 | 0.883133 | − | 0.469122i | \(-0.155430\pi\) | ||||
0.883133 | + | 0.469122i | \(0.155430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3412.00 | 0.144514 | 0.0722569 | − | 0.997386i | \(-0.476980\pi\) | ||||
0.0722569 | + | 0.997386i | \(0.476980\pi\) | |||||||
\(824\) | −4448.00 | −0.188050 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7680.00 | 0.323513 | ||||||||
\(827\) | 11300.0 | 0.475138 | 0.237569 | − | 0.971371i | \(-0.423649\pi\) | ||||
0.237569 | + | 0.971371i | \(0.423649\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26798.0 | 1.12272 | 0.561359 | − | 0.827572i | \(-0.310279\pi\) | ||||
0.561359 | + | 0.827572i | \(0.310279\pi\) | |||||||
\(830\) | −6600.00 | −0.276011 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −23994.0 | −0.998011 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1200.00 | 0.0497338 | ||||||||
\(836\) | −7168.00 | −0.296544 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1528.00 | 0.0629879 | ||||||||
\(839\) | −30744.0 | −1.26508 | −0.632539 | − | 0.774528i | \(-0.717987\pi\) | ||||
−0.632539 | + | 0.774528i | \(0.717987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16415.0 | 0.673049 | ||||||||
\(842\) | −10660.0 | −0.436304 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12752.0 | 0.520073 | ||||||||
\(845\) | 845.000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2456.00 | 0.0996330 | ||||||||
\(848\) | 4704.00 | 0.190491 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4300.00 | −0.173516 | ||||||||
\(851\) | −4488.00 | −0.180783 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11522.0 | 0.462492 | 0.231246 | − | 0.972895i | \(-0.425720\pi\) | ||||
0.231246 | + | 0.972895i | \(0.425720\pi\) | |||||||
\(854\) | −5408.00 | −0.216695 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3296.00 | 0.131606 | ||||||||
\(857\) | 10198.0 | 0.406484 | 0.203242 | − | 0.979129i | \(-0.434852\pi\) | ||||
0.203242 | + | 0.979129i | \(0.434852\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11300.0 | −0.448837 | −0.224419 | − | 0.974493i | \(-0.572048\pi\) | ||||
−0.224419 | + | 0.974493i | \(0.572048\pi\) | |||||||
\(860\) | 9200.00 | 0.364788 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22144.0 | −0.874974 | ||||||||
\(863\) | −35832.0 | −1.41337 | −0.706683 | − | 0.707530i | \(-0.749809\pi\) | ||||
−0.706683 | + | 0.707530i | \(0.749809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8150.00 | 0.320356 | ||||||||
\(866\) | −14852.0 | −0.582785 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1792.00 | 0.0700742 | ||||||||
\(869\) | 5888.00 | 0.229847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8788.00 | −0.341871 | ||||||||
\(872\) | 14512.0 | 0.563576 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7616.00 | −0.294754 | ||||||||
\(875\) | −1000.00 | −0.0386356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14518.0 | −0.558994 | −0.279497 | − | 0.960147i | \(-0.590168\pi\) | ||||
−0.279497 | + | 0.960147i | \(0.590168\pi\) | |||||||
\(878\) | −6784.00 | −0.260762 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2560.00 | 0.0980654 | ||||||||
\(881\) | 23214.0 | 0.887741 | 0.443870 | − | 0.896091i | \(-0.353605\pi\) | ||||
0.443870 | + | 0.896091i | \(0.353605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45044.0 | 1.71671 | 0.858353 | − | 0.513060i | \(-0.171488\pi\) | ||||
0.858353 | + | 0.513060i | \(0.171488\pi\) | |||||||
\(884\) | −4472.00 | −0.170147 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27944.0 | −1.05959 | ||||||||
\(887\) | −28164.0 | −1.06613 | −0.533063 | − | 0.846075i | \(-0.678959\pi\) | ||||
−0.533063 | + | 0.846075i | \(0.678959\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4064.00 | 0.153321 | ||||||||
\(890\) | −2860.00 | −0.107716 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25568.0 | 0.959731 | ||||||||
\(893\) | −1344.00 | −0.0503642 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3820.00 | −0.142669 | ||||||||
\(896\) | 1024.00 | 0.0381802 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33972.0 | 1.26243 | ||||||||
\(899\) | −11312.0 | −0.419662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25284.0 | 0.934886 | ||||||||
\(902\) | 31360.0 | 1.15762 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3632.00 | −0.133627 | ||||||||
\(905\) | 8950.00 | 0.328738 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43612.0 | 1.59660 | 0.798298 | − | 0.602263i | \(-0.205734\pi\) | ||||
0.798298 | + | 0.602263i | \(0.205734\pi\) | |||||||
\(908\) | 22992.0 | 0.840326 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1040.00 | −0.0378853 | ||||||||
\(911\) | −4056.00 | −0.147510 | −0.0737548 | − | 0.997276i | \(-0.523498\pi\) | ||||
−0.0737548 | + | 0.997276i | \(0.523498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21120.0 | 0.765575 | ||||||||
\(914\) | −3820.00 | −0.138243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9640.00 | 0.347723 | ||||||||
\(917\) | −15008.0 | −0.540467 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25976.0 | 0.932393 | 0.466197 | − | 0.884681i | \(-0.345624\pi\) | ||||
0.466197 | + | 0.884681i | \(0.345624\pi\) | |||||||
\(920\) | 2720.00 | 0.0974736 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19668.0 | 0.702528 | ||||||||
\(923\) | 1560.00 | 0.0556317 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1650.00 | 0.0586504 | ||||||||
\(926\) | 26144.0 | 0.927803 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6464.00 | −0.228654 | ||||||||
\(929\) | −46346.0 | −1.63677 | −0.818387 | − | 0.574668i | \(-0.805131\pi\) | ||||
−0.818387 | + | 0.574668i | \(0.805131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15624.0 | 0.550006 | ||||||||
\(932\) | 5432.00 | 0.190913 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39720.0 | 1.39152 | ||||||||
\(935\) | 13760.0 | 0.481284 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22694.0 | −0.791228 | −0.395614 | − | 0.918417i | \(-0.629468\pi\) | ||||
−0.395614 | + | 0.918417i | \(0.629468\pi\) | |||||||
\(938\) | 10816.0 | 0.376498 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 480.000 | 0.0166552 | ||||||||
\(941\) | −4690.00 | −0.162476 | −0.0812378 | − | 0.996695i | \(-0.525887\pi\) | ||||
−0.0812378 | + | 0.996695i | \(0.525887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33320.0 | 1.15063 | ||||||||
\(944\) | 7680.00 | 0.264791 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29440.0 | −1.01181 | ||||||||
\(947\) | 38476.0 | 1.32028 | 0.660138 | − | 0.751144i | \(-0.270498\pi\) | ||||
0.660138 | + | 0.751144i | \(0.270498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2730.00 | 0.0933820 | ||||||||
\(950\) | 2800.00 | 0.0956253 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5504.00 | 0.187380 | ||||||||
\(953\) | 11046.0 | 0.375462 | 0.187731 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187731 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12200.0 | −0.413385 | ||||||||
\(956\) | −13024.0 | −0.440613 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7344.00 | −0.247676 | ||||||||
\(959\) | 4592.00 | 0.154623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26655.0 | −0.894733 | ||||||||
\(962\) | 1716.00 | 0.0575115 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19592.0 | 0.654581 | ||||||||
\(965\) | 15510.0 | 0.517393 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3784.00 | −0.125838 | −0.0629189 | − | 0.998019i | \(-0.520041\pi\) | ||||
−0.0629189 | + | 0.998019i | \(0.520041\pi\) | |||||||
\(968\) | 2456.00 | 0.0815484 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12020.0 | 0.397875 | ||||||||
\(971\) | 19620.0 | 0.648441 | 0.324220 | − | 0.945982i | \(-0.394898\pi\) | ||||
0.324220 | + | 0.945982i | \(0.394898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14816.0 | 0.488159 | ||||||||
\(974\) | −6976.00 | −0.229492 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5408.00 | −0.177363 | ||||||||
\(977\) | −7350.00 | −0.240683 | −0.120342 | − | 0.992733i | \(-0.538399\pi\) | ||||
−0.120342 | + | 0.992733i | \(0.538399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9152.00 | 0.298773 | ||||||||
\(980\) | −5580.00 | −0.181884 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10520.0 | −0.341860 | ||||||||
\(983\) | 22008.0 | 0.714086 | 0.357043 | − | 0.934088i | \(-0.383785\pi\) | ||||
0.357043 | + | 0.934088i | \(0.383785\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9910.00 | 0.320567 | ||||||||
\(986\) | −34744.0 | −1.12218 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2912.00 | 0.0937683 | ||||||||
\(989\) | −31280.0 | −1.00571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44720.0 | −1.43348 | −0.716739 | − | 0.697341i | \(-0.754366\pi\) | ||||
−0.716739 | + | 0.697341i | \(0.754366\pi\) | |||||||
\(992\) | 1792.00 | 0.0573549 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1920.00 | −0.0612663 | ||||||||
\(995\) | −12600.0 | −0.401454 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42110.0 | −1.33765 | −0.668825 | − | 0.743420i | \(-0.733202\pi\) | ||||
−0.668825 | + | 0.743420i | \(0.733202\pi\) | |||||||
\(998\) | 16096.0 | 0.510531 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1170.4.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 130.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1040.4.a.e.1.1 | 1 | |||
15.2 | even | 4 | 650.4.b.a.599.2 | 2 | |||
15.8 | even | 4 | 650.4.b.a.599.1 | 2 | |||
15.14 | odd | 2 | 650.4.a.e.1.1 | 1 | |||
39.38 | odd | 2 | 1690.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
650.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
650.4.b.a.599.1 | 2 | 15.8 | even | 4 | |||
650.4.b.a.599.2 | 2 | 15.2 | even | 4 | |||
1040.4.a.e.1.1 | 1 | 12.11 | even | 2 | |||
1170.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1690.4.a.c.1.1 | 1 | 39.38 | odd | 2 |