Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,4,Mod(1,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("342.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.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: | \(20.1786532220\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 342.1 |
$q$-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 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.215980 | 0.107990 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107990 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −24.0000 | −0.758947 | ||||||||
\(11\) | −8.00000 | −0.219281 | −0.109640 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109640 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.0000 | −0.512031 | −0.256015 | − | 0.966673i | \(-0.582410\pi\) | ||||
−0.256015 | + | 0.966673i | \(0.582410\pi\) | |||||||
\(14\) | 8.00000 | 0.152721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −62.0000 | −0.884542 | −0.442271 | − | 0.896882i | \(-0.645827\pi\) | ||||
−0.442271 | + | 0.896882i | \(0.645827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −48.0000 | −0.536656 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.0000 | −0.155055 | ||||||||
\(23\) | −194.000 | −1.75877 | −0.879387 | − | 0.476108i | \(-0.842047\pi\) | ||||
−0.879387 | + | 0.476108i | \(0.842047\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | −48.0000 | −0.362061 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0000 | 0.107990 | ||||||||
\(29\) | −102.000 | −0.653135 | −0.326568 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326568 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | 0.104287 | 0.0521435 | − | 0.998640i | \(-0.483395\pi\) | ||||
0.0521435 | + | 0.998640i | \(0.483395\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −124.000 | −0.625465 | ||||||||
\(35\) | −48.0000 | −0.231814 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −296.000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −96.0000 | −0.379473 | ||||||||
\(41\) | −134.000 | −0.510422 | −0.255211 | − | 0.966885i | \(-0.582145\pi\) | ||||
−0.255211 | + | 0.966885i | \(0.582145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −60.0000 | −0.212789 | −0.106394 | − | 0.994324i | \(-0.533931\pi\) | ||||
−0.106394 | + | 0.994324i | \(0.533931\pi\) | |||||||
\(44\) | −32.0000 | −0.109640 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −388.000 | −1.24364 | ||||||||
\(47\) | 226.000 | 0.701393 | 0.350697 | − | 0.936489i | \(-0.385945\pi\) | ||||
0.350697 | + | 0.936489i | \(0.385945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −327.000 | −0.953353 | ||||||||
\(50\) | 38.0000 | 0.107480 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −96.0000 | −0.256015 | ||||||||
\(53\) | 362.000 | 0.938199 | 0.469099 | − | 0.883145i | \(-0.344579\pi\) | ||||
0.469099 | + | 0.883145i | \(0.344579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 96.0000 | 0.235357 | ||||||||
\(56\) | 32.0000 | 0.0763604 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −204.000 | −0.461836 | ||||||||
\(59\) | 316.000 | 0.697283 | 0.348641 | − | 0.937256i | \(-0.386643\pi\) | ||||
0.348641 | + | 0.937256i | \(0.386643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 134.000 | 0.281261 | 0.140631 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140631 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(62\) | 36.0000 | 0.0737420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 288.000 | 0.549569 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −240.000 | −0.437622 | −0.218811 | − | 0.975767i | \(-0.570218\pi\) | ||||
−0.218811 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(68\) | −248.000 | −0.442271 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −96.0000 | −0.163917 | ||||||||
\(71\) | 800.000 | 1.33722 | 0.668609 | − | 0.743614i | \(-0.266890\pi\) | ||||
0.668609 | + | 0.743614i | \(0.266890\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −578.000 | −0.926709 | −0.463355 | − | 0.886173i | \(-0.653354\pi\) | ||||
−0.463355 | + | 0.886173i | \(0.653354\pi\) | |||||||
\(74\) | −592.000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 76.0000 | 0.114708 | ||||||||
\(77\) | −32.0000 | −0.0473602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1078.00 | 1.53525 | 0.767623 | − | 0.640901i | \(-0.221439\pi\) | ||||
0.767623 | + | 0.640901i | \(0.221439\pi\) | |||||||
\(80\) | −192.000 | −0.268328 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −268.000 | −0.360923 | ||||||||
\(83\) | −940.000 | −1.24311 | −0.621557 | − | 0.783369i | \(-0.713499\pi\) | ||||
−0.621557 | + | 0.783369i | \(0.713499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 744.000 | 0.949390 | ||||||||
\(86\) | −120.000 | −0.150464 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −64.0000 | −0.0775275 | ||||||||
\(89\) | −170.000 | −0.202472 | −0.101236 | − | 0.994862i | \(-0.532280\pi\) | ||||
−0.101236 | + | 0.994862i | \(0.532280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.0000 | −0.110588 | ||||||||
\(92\) | −776.000 | −0.879387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 452.000 | 0.495960 | ||||||||
\(95\) | −228.000 | −0.246235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 206.000 | 0.215630 | 0.107815 | − | 0.994171i | \(-0.465615\pi\) | ||||
0.107815 | + | 0.994171i | \(0.465615\pi\) | |||||||
\(98\) | −654.000 | −0.674122 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 76.0000 | 0.0760000 | ||||||||
\(101\) | 884.000 | 0.870904 | 0.435452 | − | 0.900212i | \(-0.356589\pi\) | ||||
0.435452 | + | 0.900212i | \(0.356589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1146.00 | −1.09630 | −0.548149 | − | 0.836381i | \(-0.684667\pi\) | ||||
−0.548149 | + | 0.836381i | \(0.684667\pi\) | |||||||
\(104\) | −192.000 | −0.181030 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 724.000 | 0.663407 | ||||||||
\(107\) | −940.000 | −0.849283 | −0.424641 | − | 0.905362i | \(-0.639600\pi\) | ||||
−0.424641 | + | 0.905362i | \(0.639600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −892.000 | −0.783836 | −0.391918 | − | 0.920000i | \(-0.628188\pi\) | ||||
−0.391918 | + | 0.920000i | \(0.628188\pi\) | |||||||
\(110\) | 192.000 | 0.166423 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 64.0000 | 0.0539949 | ||||||||
\(113\) | 1858.00 | 1.54678 | 0.773389 | − | 0.633932i | \(-0.218560\pi\) | ||||
0.773389 | + | 0.633932i | \(0.218560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2328.00 | 1.88771 | ||||||||
\(116\) | −408.000 | −0.326568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 632.000 | 0.493054 | ||||||||
\(119\) | −248.000 | −0.191043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | 268.000 | 0.198882 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 72.0000 | 0.0521435 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 322.000 | 0.224983 | 0.112492 | − | 0.993653i | \(-0.464117\pi\) | ||||
0.112492 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 576.000 | 0.388604 | ||||||||
\(131\) | 1500.00 | 1.00042 | 0.500212 | − | 0.865903i | \(-0.333255\pi\) | ||||
0.500212 | + | 0.865903i | \(0.333255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 76.0000 | 0.0495491 | ||||||||
\(134\) | −480.000 | −0.309445 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −496.000 | −0.312733 | ||||||||
\(137\) | 1146.00 | 0.714667 | 0.357334 | − | 0.933977i | \(-0.383686\pi\) | ||||
0.357334 | + | 0.933977i | \(0.383686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1364.00 | 0.832324 | 0.416162 | − | 0.909291i | \(-0.363375\pi\) | ||||
0.416162 | + | 0.909291i | \(0.363375\pi\) | |||||||
\(140\) | −192.000 | −0.115907 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1600.00 | 0.945556 | ||||||||
\(143\) | 192.000 | 0.112279 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1224.00 | 0.701018 | ||||||||
\(146\) | −1156.00 | −0.655282 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1184.00 | −0.657596 | ||||||||
\(149\) | −1168.00 | −0.642190 | −0.321095 | − | 0.947047i | \(-0.604051\pi\) | ||||
−0.321095 | + | 0.947047i | \(0.604051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1270.00 | 0.684445 | 0.342222 | − | 0.939619i | \(-0.388820\pi\) | ||||
0.342222 | + | 0.939619i | \(0.388820\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −64.0000 | −0.0334887 | ||||||||
\(155\) | −216.000 | −0.111933 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1182.00 | −0.600853 | −0.300426 | − | 0.953805i | \(-0.597129\pi\) | ||||
−0.300426 | + | 0.953805i | \(0.597129\pi\) | |||||||
\(158\) | 2156.00 | 1.08558 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −384.000 | −0.189737 | ||||||||
\(161\) | −776.000 | −0.379859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 764.000 | 0.367123 | 0.183562 | − | 0.983008i | \(-0.441237\pi\) | ||||
0.183562 | + | 0.983008i | \(0.441237\pi\) | |||||||
\(164\) | −536.000 | −0.255211 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1880.00 | −0.879014 | ||||||||
\(167\) | −1284.00 | −0.594963 | −0.297482 | − | 0.954728i | \(-0.596147\pi\) | ||||
−0.297482 | + | 0.954728i | \(0.596147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1621.00 | −0.737824 | ||||||||
\(170\) | 1488.00 | 0.671320 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −240.000 | −0.106394 | ||||||||
\(173\) | 4134.00 | 1.81678 | 0.908388 | − | 0.418129i | \(-0.137314\pi\) | ||||
0.908388 | + | 0.418129i | \(0.137314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 76.0000 | 0.0328289 | ||||||||
\(176\) | −128.000 | −0.0548202 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −340.000 | −0.143169 | ||||||||
\(179\) | −2660.00 | −1.11071 | −0.555357 | − | 0.831612i | \(-0.687418\pi\) | ||||
−0.555357 | + | 0.831612i | \(0.687418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2340.00 | 0.960944 | 0.480472 | − | 0.877010i | \(-0.340465\pi\) | ||||
0.480472 | + | 0.877010i | \(0.340465\pi\) | |||||||
\(182\) | −192.000 | −0.0781977 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1552.00 | −0.621820 | ||||||||
\(185\) | 3552.00 | 1.41161 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 496.000 | 0.193963 | ||||||||
\(188\) | 904.000 | 0.350697 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −456.000 | −0.174114 | ||||||||
\(191\) | −3818.00 | −1.44639 | −0.723196 | − | 0.690643i | \(-0.757328\pi\) | ||||
−0.723196 | + | 0.690643i | \(0.757328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1330.00 | −0.496039 | −0.248019 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248019 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(194\) | 412.000 | 0.152474 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1308.00 | −0.476676 | ||||||||
\(197\) | −2432.00 | −0.879557 | −0.439779 | − | 0.898106i | \(-0.644943\pi\) | ||||
−0.439779 | + | 0.898106i | \(0.644943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3788.00 | 1.34937 | 0.674684 | − | 0.738107i | \(-0.264280\pi\) | ||||
0.674684 | + | 0.738107i | \(0.264280\pi\) | |||||||
\(200\) | 152.000 | 0.0537401 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1768.00 | 0.615822 | ||||||||
\(203\) | −408.000 | −0.141064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1608.00 | 0.547842 | ||||||||
\(206\) | −2292.00 | −0.775200 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −384.000 | −0.128008 | ||||||||
\(209\) | −152.000 | −0.0503065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1868.00 | −0.609471 | −0.304736 | − | 0.952437i | \(-0.598568\pi\) | ||||
−0.304736 | + | 0.952437i | \(0.598568\pi\) | |||||||
\(212\) | 1448.00 | 0.469099 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1880.00 | −0.600533 | ||||||||
\(215\) | 720.000 | 0.228389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 72.0000 | 0.0225239 | ||||||||
\(218\) | −1784.00 | −0.554256 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 384.000 | 0.117679 | ||||||||
\(221\) | 1488.00 | 0.452913 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3990.00 | −1.19816 | −0.599081 | − | 0.800688i | \(-0.704467\pi\) | ||||
−0.599081 | + | 0.800688i | \(0.704467\pi\) | |||||||
\(224\) | 128.000 | 0.0381802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3716.00 | 1.09374 | ||||||||
\(227\) | 3596.00 | 1.05143 | 0.525716 | − | 0.850660i | \(-0.323798\pi\) | ||||
0.525716 | + | 0.850660i | \(0.323798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5518.00 | 1.59231 | 0.796157 | − | 0.605091i | \(-0.206863\pi\) | ||||
0.796157 | + | 0.605091i | \(0.206863\pi\) | |||||||
\(230\) | 4656.00 | 1.33482 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −816.000 | −0.230918 | ||||||||
\(233\) | −138.000 | −0.0388012 | −0.0194006 | − | 0.999812i | \(-0.506176\pi\) | ||||
−0.0194006 | + | 0.999812i | \(0.506176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2712.00 | −0.752814 | ||||||||
\(236\) | 1264.00 | 0.348641 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −496.000 | −0.135088 | ||||||||
\(239\) | −6870.00 | −1.85934 | −0.929672 | − | 0.368388i | \(-0.879910\pi\) | ||||
−0.929672 | + | 0.368388i | \(0.879910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5830.00 | 1.55827 | 0.779136 | − | 0.626856i | \(-0.215658\pi\) | ||||
0.779136 | + | 0.626856i | \(0.215658\pi\) | |||||||
\(242\) | −2534.00 | −0.673106 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 536.000 | 0.140631 | ||||||||
\(245\) | 3924.00 | 1.02325 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −456.000 | −0.117468 | ||||||||
\(248\) | 144.000 | 0.0368710 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2544.00 | 0.643587 | ||||||||
\(251\) | −564.000 | −0.141830 | −0.0709151 | − | 0.997482i | \(-0.522592\pi\) | ||||
−0.0709151 | + | 0.997482i | \(0.522592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1552.00 | 0.385666 | ||||||||
\(254\) | 644.000 | 0.159087 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1842.00 | −0.447085 | −0.223542 | − | 0.974694i | \(-0.571762\pi\) | ||||
−0.223542 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1184.00 | −0.284055 | ||||||||
\(260\) | 1152.00 | 0.274785 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3000.00 | 0.707407 | ||||||||
\(263\) | −3702.00 | −0.867966 | −0.433983 | − | 0.900921i | \(-0.642892\pi\) | ||||
−0.433983 | + | 0.900921i | \(0.642892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4344.00 | −1.00698 | ||||||||
\(266\) | 152.000 | 0.0350365 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −960.000 | −0.218811 | ||||||||
\(269\) | −6130.00 | −1.38942 | −0.694708 | − | 0.719292i | \(-0.744466\pi\) | ||||
−0.694708 | + | 0.719292i | \(0.744466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7300.00 | −1.63632 | −0.818161 | − | 0.574989i | \(-0.805006\pi\) | ||||
−0.818161 | + | 0.574989i | \(0.805006\pi\) | |||||||
\(272\) | −992.000 | −0.221135 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2292.00 | 0.505346 | ||||||||
\(275\) | −152.000 | −0.0333307 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7822.00 | 1.69667 | 0.848337 | − | 0.529457i | \(-0.177604\pi\) | ||||
0.848337 | + | 0.529457i | \(0.177604\pi\) | |||||||
\(278\) | 2728.00 | 0.588542 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −384.000 | −0.0819585 | ||||||||
\(281\) | −3278.00 | −0.695904 | −0.347952 | − | 0.937512i | \(-0.613123\pi\) | ||||
−0.347952 | + | 0.937512i | \(0.613123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5636.00 | −1.18384 | −0.591918 | − | 0.805998i | \(-0.701629\pi\) | ||||
−0.591918 | + | 0.805998i | \(0.701629\pi\) | |||||||
\(284\) | 3200.00 | 0.668609 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 384.000 | 0.0793930 | ||||||||
\(287\) | −536.000 | −0.110241 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1069.00 | −0.217586 | ||||||||
\(290\) | 2448.00 | 0.495695 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2312.00 | −0.463355 | ||||||||
\(293\) | 7310.00 | 1.45752 | 0.728762 | − | 0.684767i | \(-0.240096\pi\) | ||||
0.728762 | + | 0.684767i | \(0.240096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3792.00 | −0.748403 | ||||||||
\(296\) | −2368.00 | −0.464991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2336.00 | −0.454097 | ||||||||
\(299\) | 4656.00 | 0.900547 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −240.000 | −0.0459580 | ||||||||
\(302\) | 2540.00 | 0.483975 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 304.000 | 0.0573539 | ||||||||
\(305\) | −1608.00 | −0.301881 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4008.00 | −0.745110 | −0.372555 | − | 0.928010i | \(-0.621518\pi\) | ||||
−0.372555 | + | 0.928010i | \(0.621518\pi\) | |||||||
\(308\) | −128.000 | −0.0236801 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −432.000 | −0.0791482 | ||||||||
\(311\) | −6182.00 | −1.12717 | −0.563584 | − | 0.826059i | \(-0.690578\pi\) | ||||
−0.563584 | + | 0.826059i | \(0.690578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9594.00 | −1.73254 | −0.866270 | − | 0.499576i | \(-0.833489\pi\) | ||||
−0.866270 | + | 0.499576i | \(0.833489\pi\) | |||||||
\(314\) | −2364.00 | −0.424867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4312.00 | 0.767623 | ||||||||
\(317\) | −2874.00 | −0.509211 | −0.254606 | − | 0.967045i | \(-0.581946\pi\) | ||||
−0.254606 | + | 0.967045i | \(0.581946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 816.000 | 0.143220 | ||||||||
\(320\) | −768.000 | −0.134164 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1552.00 | −0.268601 | ||||||||
\(323\) | −1178.00 | −0.202928 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −456.000 | −0.0778287 | ||||||||
\(326\) | 1528.00 | 0.259595 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1072.00 | −0.180461 | ||||||||
\(329\) | 904.000 | 0.151487 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6240.00 | −1.03620 | −0.518099 | − | 0.855321i | \(-0.673360\pi\) | ||||
−0.518099 | + | 0.855321i | \(0.673360\pi\) | |||||||
\(332\) | −3760.00 | −0.621557 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2568.00 | −0.420703 | ||||||||
\(335\) | 2880.00 | 0.469705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10126.0 | −1.63679 | −0.818395 | − | 0.574656i | \(-0.805136\pi\) | ||||
−0.818395 | + | 0.574656i | \(0.805136\pi\) | |||||||
\(338\) | −3242.00 | −0.521721 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2976.00 | 0.474695 | ||||||||
\(341\) | −144.000 | −0.0228681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2680.00 | −0.421885 | ||||||||
\(344\) | −480.000 | −0.0752322 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8268.00 | 1.28465 | ||||||||
\(347\) | 3376.00 | 0.522286 | 0.261143 | − | 0.965300i | \(-0.415901\pi\) | ||||
0.261143 | + | 0.965300i | \(0.415901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9806.00 | −1.50402 | −0.752010 | − | 0.659151i | \(-0.770916\pi\) | ||||
−0.752010 | + | 0.659151i | \(0.770916\pi\) | |||||||
\(350\) | 152.000 | 0.0232135 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −256.000 | −0.0387638 | ||||||||
\(353\) | −9402.00 | −1.41761 | −0.708807 | − | 0.705402i | \(-0.750766\pi\) | ||||
−0.708807 | + | 0.705402i | \(0.750766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9600.00 | −1.43525 | ||||||||
\(356\) | −680.000 | −0.101236 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5320.00 | −0.785393 | ||||||||
\(359\) | −11010.0 | −1.61862 | −0.809311 | − | 0.587380i | \(-0.800159\pi\) | ||||
−0.809311 | + | 0.587380i | \(0.800159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 4680.00 | 0.679490 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −384.000 | −0.0552941 | ||||||||
\(365\) | 6936.00 | 0.994649 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9956.00 | 1.41607 | 0.708037 | − | 0.706176i | \(-0.249581\pi\) | ||||
0.708037 | + | 0.706176i | \(0.249581\pi\) | |||||||
\(368\) | −3104.00 | −0.439693 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7104.00 | 0.998160 | ||||||||
\(371\) | 1448.00 | 0.202632 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2024.00 | 0.280962 | 0.140481 | − | 0.990083i | \(-0.455135\pi\) | ||||
0.140481 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(374\) | 992.000 | 0.137153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1808.00 | 0.247980 | ||||||||
\(377\) | 2448.00 | 0.334426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8560.00 | −1.16015 | −0.580076 | − | 0.814562i | \(-0.696977\pi\) | ||||
−0.580076 | + | 0.814562i | \(0.696977\pi\) | |||||||
\(380\) | −912.000 | −0.123117 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7636.00 | −1.02275 | ||||||||
\(383\) | 3944.00 | 0.526185 | 0.263093 | − | 0.964771i | \(-0.415258\pi\) | ||||
0.263093 | + | 0.964771i | \(0.415258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 384.000 | 0.0508323 | ||||||||
\(386\) | −2660.00 | −0.350752 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 824.000 | 0.107815 | ||||||||
\(389\) | 1964.00 | 0.255987 | 0.127993 | − | 0.991775i | \(-0.459146\pi\) | ||||
0.127993 | + | 0.991775i | \(0.459146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12028.0 | 1.55571 | ||||||||
\(392\) | −2616.00 | −0.337061 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4864.00 | −0.621941 | ||||||||
\(395\) | −12936.0 | −1.64780 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7434.00 | 0.939803 | 0.469901 | − | 0.882719i | \(-0.344289\pi\) | ||||
0.469901 | + | 0.882719i | \(0.344289\pi\) | |||||||
\(398\) | 7576.00 | 0.954147 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 304.000 | 0.0380000 | ||||||||
\(401\) | 7026.00 | 0.874967 | 0.437483 | − | 0.899226i | \(-0.355870\pi\) | ||||
0.437483 | + | 0.899226i | \(0.355870\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −432.000 | −0.0533981 | ||||||||
\(404\) | 3536.00 | 0.435452 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −816.000 | −0.0997473 | ||||||||
\(407\) | 2368.00 | 0.288397 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8454.00 | 1.02206 | 0.511031 | − | 0.859562i | \(-0.329264\pi\) | ||||
0.511031 | + | 0.859562i | \(0.329264\pi\) | |||||||
\(410\) | 3216.00 | 0.387383 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4584.00 | −0.548149 | ||||||||
\(413\) | 1264.00 | 0.150599 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11280.0 | 1.33425 | ||||||||
\(416\) | −768.000 | −0.0905151 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −304.000 | −0.0355721 | ||||||||
\(419\) | 12552.0 | 1.46350 | 0.731749 | − | 0.681575i | \(-0.238705\pi\) | ||||
0.731749 | + | 0.681575i | \(0.238705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13120.0 | 1.51884 | 0.759418 | − | 0.650603i | \(-0.225484\pi\) | ||||
0.759418 | + | 0.650603i | \(0.225484\pi\) | |||||||
\(422\) | −3736.00 | −0.430961 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2896.00 | 0.331703 | ||||||||
\(425\) | −1178.00 | −0.134450 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 536.000 | 0.0607467 | ||||||||
\(428\) | −3760.00 | −0.424641 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1440.00 | 0.161495 | ||||||||
\(431\) | −12388.0 | −1.38448 | −0.692238 | − | 0.721669i | \(-0.743375\pi\) | ||||
−0.692238 | + | 0.721669i | \(0.743375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7182.00 | 0.797101 | 0.398551 | − | 0.917146i | \(-0.369513\pi\) | ||||
0.398551 | + | 0.917146i | \(0.369513\pi\) | |||||||
\(434\) | 144.000 | 0.0159268 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3568.00 | −0.391918 | ||||||||
\(437\) | −3686.00 | −0.403490 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16090.0 | 1.74928 | 0.874640 | − | 0.484773i | \(-0.161098\pi\) | ||||
0.874640 | + | 0.484773i | \(0.161098\pi\) | |||||||
\(440\) | 768.000 | 0.0832113 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2976.00 | 0.320258 | ||||||||
\(443\) | 2544.00 | 0.272842 | 0.136421 | − | 0.990651i | \(-0.456440\pi\) | ||||
0.136421 | + | 0.990651i | \(0.456440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2040.00 | 0.217315 | ||||||||
\(446\) | −7980.00 | −0.847229 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 256.000 | 0.0269975 | ||||||||
\(449\) | −4338.00 | −0.455953 | −0.227976 | − | 0.973667i | \(-0.573211\pi\) | ||||
−0.227976 | + | 0.973667i | \(0.573211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1072.00 | 0.111926 | ||||||||
\(452\) | 7432.00 | 0.773389 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7192.00 | 0.743474 | ||||||||
\(455\) | 1152.00 | 0.118696 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10274.0 | 1.05164 | 0.525818 | − | 0.850597i | \(-0.323759\pi\) | ||||
0.525818 | + | 0.850597i | \(0.323759\pi\) | |||||||
\(458\) | 11036.0 | 1.12594 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9312.00 | 0.943857 | ||||||||
\(461\) | −768.000 | −0.0775907 | −0.0387954 | − | 0.999247i | \(-0.512352\pi\) | ||||
−0.0387954 | + | 0.999247i | \(0.512352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11148.0 | −1.11899 | −0.559494 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559494 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(464\) | −1632.00 | −0.163284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −276.000 | −0.0274366 | ||||||||
\(467\) | −18532.0 | −1.83631 | −0.918157 | − | 0.396217i | \(-0.870323\pi\) | ||||
−0.918157 | + | 0.396217i | \(0.870323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −960.000 | −0.0945174 | ||||||||
\(470\) | −5424.00 | −0.532320 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2528.00 | 0.246527 | ||||||||
\(473\) | 480.000 | 0.0466605 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 361.000 | 0.0348712 | ||||||||
\(476\) | −992.000 | −0.0955215 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13740.0 | −1.31476 | ||||||||
\(479\) | 6942.00 | 0.662188 | 0.331094 | − | 0.943598i | \(-0.392582\pi\) | ||||
0.331094 | + | 0.943598i | \(0.392582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7104.00 | 0.673419 | ||||||||
\(482\) | 11660.0 | 1.10186 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5068.00 | −0.475958 | ||||||||
\(485\) | −2472.00 | −0.231439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9370.00 | −0.871859 | −0.435929 | − | 0.899981i | \(-0.643580\pi\) | ||||
−0.435929 | + | 0.899981i | \(0.643580\pi\) | |||||||
\(488\) | 1072.00 | 0.0994409 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7848.00 | 0.723544 | ||||||||
\(491\) | 13572.0 | 1.24745 | 0.623723 | − | 0.781646i | \(-0.285619\pi\) | ||||
0.623723 | + | 0.781646i | \(0.285619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6324.00 | 0.577725 | ||||||||
\(494\) | −912.000 | −0.0830624 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 288.000 | 0.0260717 | ||||||||
\(497\) | 3200.00 | 0.288812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −124.000 | −0.0111243 | −0.00556213 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556213 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(500\) | 5088.00 | 0.455085 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1128.00 | −0.100289 | ||||||||
\(503\) | −638.000 | −0.0565547 | −0.0282773 | − | 0.999600i | \(-0.509002\pi\) | ||||
−0.0282773 | + | 0.999600i | \(0.509002\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10608.0 | −0.934752 | ||||||||
\(506\) | 3104.00 | 0.272707 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1288.00 | 0.112492 | ||||||||
\(509\) | 9758.00 | 0.849736 | 0.424868 | − | 0.905255i | \(-0.360320\pi\) | ||||
0.424868 | + | 0.905255i | \(0.360320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2312.00 | −0.200150 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3684.00 | −0.316137 | ||||||||
\(515\) | 13752.0 | 1.17667 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1808.00 | −0.153802 | ||||||||
\(518\) | −2368.00 | −0.200857 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2304.00 | 0.194302 | ||||||||
\(521\) | 4750.00 | 0.399427 | 0.199713 | − | 0.979854i | \(-0.435999\pi\) | ||||
0.199713 | + | 0.979854i | \(0.435999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18080.0 | −1.51163 | −0.755816 | − | 0.654784i | \(-0.772759\pi\) | ||||
−0.755816 | + | 0.654784i | \(0.772759\pi\) | |||||||
\(524\) | 6000.00 | 0.500212 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7404.00 | −0.613745 | ||||||||
\(527\) | −1116.00 | −0.0922462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25469.0 | 2.09329 | ||||||||
\(530\) | −8688.00 | −0.712043 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 304.000 | 0.0247746 | ||||||||
\(533\) | 3216.00 | 0.261352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11280.0 | 0.911546 | ||||||||
\(536\) | −1920.00 | −0.154723 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12260.0 | −0.982465 | ||||||||
\(539\) | 2616.00 | 0.209052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3478.00 | −0.276397 | −0.138199 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138199 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(542\) | −14600.0 | −1.15705 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1984.00 | −0.156366 | ||||||||
\(545\) | 10704.0 | 0.841301 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13832.0 | 1.08119 | 0.540597 | − | 0.841281i | \(-0.318198\pi\) | ||||
0.540597 | + | 0.841281i | \(0.318198\pi\) | |||||||
\(548\) | 4584.00 | 0.357334 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −304.000 | −0.0235684 | ||||||||
\(551\) | −1938.00 | −0.149840 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4312.00 | 0.331582 | ||||||||
\(554\) | 15644.0 | 1.19973 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5456.00 | 0.416162 | ||||||||
\(557\) | 17296.0 | 1.31572 | 0.657859 | − | 0.753141i | \(-0.271462\pi\) | ||||
0.657859 | + | 0.753141i | \(0.271462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1440.00 | 0.108954 | ||||||||
\(560\) | −768.000 | −0.0579534 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6556.00 | −0.492079 | ||||||||
\(563\) | 2196.00 | 0.164388 | 0.0821939 | − | 0.996616i | \(-0.473807\pi\) | ||||
0.0821939 | + | 0.996616i | \(0.473807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22296.0 | −1.66018 | ||||||||
\(566\) | −11272.0 | −0.837098 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6400.00 | 0.472778 | ||||||||
\(569\) | −25386.0 | −1.87036 | −0.935181 | − | 0.354169i | \(-0.884764\pi\) | ||||
−0.935181 | + | 0.354169i | \(0.884764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1196.00 | 0.0876551 | 0.0438275 | − | 0.999039i | \(-0.486045\pi\) | ||||
0.0438275 | + | 0.999039i | \(0.486045\pi\) | |||||||
\(572\) | 768.000 | 0.0561393 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1072.00 | −0.0779519 | ||||||||
\(575\) | −3686.00 | −0.267334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7934.00 | −0.572438 | −0.286219 | − | 0.958164i | \(-0.592398\pi\) | ||||
−0.286219 | + | 0.958164i | \(0.592398\pi\) | |||||||
\(578\) | −2138.00 | −0.153857 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4896.00 | 0.350509 | ||||||||
\(581\) | −3760.00 | −0.268487 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2896.00 | −0.205729 | ||||||||
\(584\) | −4624.00 | −0.327641 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14620.0 | 1.03063 | ||||||||
\(587\) | 22120.0 | 1.55535 | 0.777675 | − | 0.628667i | \(-0.216399\pi\) | ||||
0.777675 | + | 0.628667i | \(0.216399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 342.000 | 0.0239251 | ||||||||
\(590\) | −7584.00 | −0.529201 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4736.00 | −0.328798 | ||||||||
\(593\) | −9722.00 | −0.673246 | −0.336623 | − | 0.941640i | \(-0.609285\pi\) | ||||
−0.336623 | + | 0.941640i | \(0.609285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2976.00 | 0.205049 | ||||||||
\(596\) | −4672.00 | −0.321095 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9312.00 | 0.636783 | ||||||||
\(599\) | 9980.00 | 0.680754 | 0.340377 | − | 0.940289i | \(-0.389445\pi\) | ||||
0.340377 | + | 0.940289i | \(0.389445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6138.00 | 0.416596 | 0.208298 | − | 0.978065i | \(-0.433208\pi\) | ||||
0.208298 | + | 0.978065i | \(0.433208\pi\) | |||||||
\(602\) | −480.000 | −0.0324972 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5080.00 | 0.342222 | ||||||||
\(605\) | 15204.0 | 1.02170 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10286.0 | 0.687802 | 0.343901 | − | 0.939006i | \(-0.388252\pi\) | ||||
0.343901 | + | 0.939006i | \(0.388252\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3216.00 | −0.213462 | ||||||||
\(611\) | −5424.00 | −0.359135 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4178.00 | 0.275282 | 0.137641 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137641 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(614\) | −8016.00 | −0.526872 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −256.000 | −0.0167444 | ||||||||
\(617\) | 19086.0 | 1.24534 | 0.622669 | − | 0.782485i | \(-0.286048\pi\) | ||||
0.622669 | + | 0.782485i | \(0.286048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11084.0 | −0.719715 | −0.359857 | − | 0.933007i | \(-0.617175\pi\) | ||||
−0.359857 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(620\) | −864.000 | −0.0559663 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12364.0 | −0.797028 | ||||||||
\(623\) | −680.000 | −0.0437297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | −19188.0 | −1.22509 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4728.00 | −0.300426 | ||||||||
\(629\) | 18352.0 | 1.16334 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9160.00 | −0.577898 | −0.288949 | − | 0.957344i | \(-0.593306\pi\) | ||||
−0.288949 | + | 0.957344i | \(0.593306\pi\) | |||||||
\(632\) | 8624.00 | 0.542792 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5748.00 | −0.360067 | ||||||||
\(635\) | −3864.00 | −0.241477 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7848.00 | 0.488146 | ||||||||
\(638\) | 1632.00 | 0.101272 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1536.00 | −0.0948683 | ||||||||
\(641\) | −13082.0 | −0.806097 | −0.403048 | − | 0.915179i | \(-0.632049\pi\) | ||||
−0.403048 | + | 0.915179i | \(0.632049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7852.00 | 0.481575 | 0.240787 | − | 0.970578i | \(-0.422594\pi\) | ||||
0.240787 | + | 0.970578i | \(0.422594\pi\) | |||||||
\(644\) | −3104.00 | −0.189930 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2356.00 | −0.143492 | ||||||||
\(647\) | −10530.0 | −0.639841 | −0.319920 | − | 0.947444i | \(-0.603656\pi\) | ||||
−0.319920 | + | 0.947444i | \(0.603656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2528.00 | −0.152901 | ||||||||
\(650\) | −912.000 | −0.0550332 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3056.00 | 0.183562 | ||||||||
\(653\) | 17880.0 | 1.07151 | 0.535757 | − | 0.844372i | \(-0.320026\pi\) | ||||
0.535757 | + | 0.844372i | \(0.320026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18000.0 | −1.07377 | ||||||||
\(656\) | −2144.00 | −0.127605 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1808.00 | 0.107117 | ||||||||
\(659\) | −27404.0 | −1.61989 | −0.809946 | − | 0.586505i | \(-0.800503\pi\) | ||||
−0.809946 | + | 0.586505i | \(0.800503\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22936.0 | 1.34963 | 0.674816 | − | 0.737986i | \(-0.264223\pi\) | ||||
0.674816 | + | 0.737986i | \(0.264223\pi\) | |||||||
\(662\) | −12480.0 | −0.732702 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7520.00 | −0.439507 | ||||||||
\(665\) | −912.000 | −0.0531817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19788.0 | 1.14872 | ||||||||
\(668\) | −5136.00 | −0.297482 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5760.00 | 0.332132 | ||||||||
\(671\) | −1072.00 | −0.0616753 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25762.0 | −1.47556 | −0.737780 | − | 0.675041i | \(-0.764126\pi\) | ||||
−0.737780 | + | 0.675041i | \(0.764126\pi\) | |||||||
\(674\) | −20252.0 | −1.15739 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6484.00 | −0.368912 | ||||||||
\(677\) | −11214.0 | −0.636616 | −0.318308 | − | 0.947987i | \(-0.603115\pi\) | ||||
−0.318308 | + | 0.947987i | \(0.603115\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 824.000 | 0.0465717 | ||||||||
\(680\) | 5952.00 | 0.335660 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −288.000 | −0.0161702 | ||||||||
\(683\) | −15516.0 | −0.869258 | −0.434629 | − | 0.900610i | \(-0.643121\pi\) | ||||
−0.434629 | + | 0.900610i | \(0.643121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13752.0 | −0.767061 | ||||||||
\(686\) | −5360.00 | −0.298317 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −960.000 | −0.0531972 | ||||||||
\(689\) | −8688.00 | −0.480387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13028.0 | −0.717234 | −0.358617 | − | 0.933485i | \(-0.616752\pi\) | ||||
−0.358617 | + | 0.933485i | \(0.616752\pi\) | |||||||
\(692\) | 16536.0 | 0.908388 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6752.00 | 0.369312 | ||||||||
\(695\) | −16368.0 | −0.893343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8308.00 | 0.451489 | ||||||||
\(698\) | −19612.0 | −1.06350 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 304.000 | 0.0164145 | ||||||||
\(701\) | 14404.0 | 0.776079 | 0.388040 | − | 0.921643i | \(-0.373152\pi\) | ||||
0.388040 | + | 0.921643i | \(0.373152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5624.00 | −0.301726 | ||||||||
\(704\) | −512.000 | −0.0274101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18804.0 | −1.00240 | ||||||||
\(707\) | 3536.00 | 0.188098 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13070.0 | 0.692319 | 0.346159 | − | 0.938176i | \(-0.387486\pi\) | ||||
0.346159 | + | 0.938176i | \(0.387486\pi\) | |||||||
\(710\) | −19200.0 | −1.01488 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1360.00 | −0.0715845 | ||||||||
\(713\) | −3492.00 | −0.183417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2304.00 | −0.120510 | ||||||||
\(716\) | −10640.0 | −0.555357 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22020.0 | −1.14454 | ||||||||
\(719\) | 7450.00 | 0.386423 | 0.193211 | − | 0.981157i | \(-0.438110\pi\) | ||||
0.193211 | + | 0.981157i | \(0.438110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4584.00 | −0.236778 | ||||||||
\(722\) | 722.000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9360.00 | 0.480472 | ||||||||
\(725\) | −1938.00 | −0.0992766 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23792.0 | 1.21375 | 0.606875 | − | 0.794797i | \(-0.292423\pi\) | ||||
0.606875 | + | 0.794797i | \(0.292423\pi\) | |||||||
\(728\) | −768.000 | −0.0390989 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13872.0 | 0.703323 | ||||||||
\(731\) | 3720.00 | 0.188220 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29390.0 | −1.48096 | −0.740481 | − | 0.672078i | \(-0.765402\pi\) | ||||
−0.740481 | + | 0.672078i | \(0.765402\pi\) | |||||||
\(734\) | 19912.0 | 1.00132 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6208.00 | −0.310910 | ||||||||
\(737\) | 1920.00 | 0.0959622 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22580.0 | −1.12398 | −0.561988 | − | 0.827145i | \(-0.689963\pi\) | ||||
−0.561988 | + | 0.827145i | \(0.689963\pi\) | |||||||
\(740\) | 14208.0 | 0.705806 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2896.00 | 0.143282 | ||||||||
\(743\) | −21732.0 | −1.07304 | −0.536521 | − | 0.843887i | \(-0.680262\pi\) | ||||
−0.536521 | + | 0.843887i | \(0.680262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14016.0 | 0.689270 | ||||||||
\(746\) | 4048.00 | 0.198670 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1984.00 | 0.0969816 | ||||||||
\(749\) | −3760.00 | −0.183428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19754.0 | −0.959832 | −0.479916 | − | 0.877314i | \(-0.659333\pi\) | ||||
−0.479916 | + | 0.877314i | \(0.659333\pi\) | |||||||
\(752\) | 3616.00 | 0.175348 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4896.00 | 0.236475 | ||||||||
\(755\) | −15240.0 | −0.734623 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5662.00 | −0.271848 | −0.135924 | − | 0.990719i | \(-0.543400\pi\) | ||||
−0.135924 | + | 0.990719i | \(0.543400\pi\) | |||||||
\(758\) | −17120.0 | −0.820351 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1824.00 | −0.0870572 | ||||||||
\(761\) | 6818.00 | 0.324773 | 0.162387 | − | 0.986727i | \(-0.448081\pi\) | ||||
0.162387 | + | 0.986727i | \(0.448081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3568.00 | −0.169293 | ||||||||
\(764\) | −15272.0 | −0.723196 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7888.00 | 0.372069 | ||||||||
\(767\) | −7584.00 | −0.357030 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7986.00 | −0.374490 | −0.187245 | − | 0.982313i | \(-0.559956\pi\) | ||||
−0.187245 | + | 0.982313i | \(0.559956\pi\) | |||||||
\(770\) | 768.000 | 0.0359439 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5320.00 | −0.248019 | ||||||||
\(773\) | −21666.0 | −1.00811 | −0.504057 | − | 0.863670i | \(-0.668160\pi\) | ||||
−0.504057 | + | 0.863670i | \(0.668160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 342.000 | 0.0158516 | ||||||||
\(776\) | 1648.00 | 0.0762368 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3928.00 | 0.181010 | ||||||||
\(779\) | −2546.00 | −0.117099 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6400.00 | −0.293227 | ||||||||
\(782\) | 24056.0 | 1.10005 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5232.00 | −0.238338 | ||||||||
\(785\) | 14184.0 | 0.644903 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10628.0 | −0.481382 | −0.240691 | − | 0.970602i | \(-0.577374\pi\) | ||||
−0.240691 | + | 0.970602i | \(0.577374\pi\) | |||||||
\(788\) | −9728.00 | −0.439779 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25872.0 | −1.16517 | ||||||||
\(791\) | 7432.00 | 0.334073 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3216.00 | −0.144015 | ||||||||
\(794\) | 14868.0 | 0.664541 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15152.0 | 0.674684 | ||||||||
\(797\) | −1450.00 | −0.0644437 | −0.0322219 | − | 0.999481i | \(-0.510258\pi\) | ||||
−0.0322219 | + | 0.999481i | \(0.510258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14012.0 | −0.620412 | ||||||||
\(800\) | 608.000 | 0.0268701 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14052.0 | 0.618695 | ||||||||
\(803\) | 4624.00 | 0.203210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9312.00 | 0.407708 | ||||||||
\(806\) | −864.000 | −0.0377582 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7072.00 | 0.307911 | ||||||||
\(809\) | 32850.0 | 1.42762 | 0.713810 | − | 0.700339i | \(-0.246968\pi\) | ||||
0.713810 | + | 0.700339i | \(0.246968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2744.00 | −0.118810 | −0.0594050 | − | 0.998234i | \(-0.518920\pi\) | ||||
−0.0594050 | + | 0.998234i | \(0.518920\pi\) | |||||||
\(812\) | −1632.00 | −0.0705320 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4736.00 | 0.203927 | ||||||||
\(815\) | −9168.00 | −0.394038 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1140.00 | −0.0488171 | ||||||||
\(818\) | 16908.0 | 0.722707 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6432.00 | 0.273921 | ||||||||
\(821\) | 13884.0 | 0.590201 | 0.295100 | − | 0.955466i | \(-0.404647\pi\) | ||||
0.295100 | + | 0.955466i | \(0.404647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20968.0 | 0.888091 | 0.444045 | − | 0.896004i | \(-0.353543\pi\) | ||||
0.444045 | + | 0.896004i | \(0.353543\pi\) | |||||||
\(824\) | −9168.00 | −0.387600 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2528.00 | 0.106490 | ||||||||
\(827\) | 12516.0 | 0.526268 | 0.263134 | − | 0.964759i | \(-0.415244\pi\) | ||||
0.263134 | + | 0.964759i | \(0.415244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22484.0 | 0.941980 | 0.470990 | − | 0.882138i | \(-0.343897\pi\) | ||||
0.470990 | + | 0.882138i | \(0.343897\pi\) | |||||||
\(830\) | 22560.0 | 0.943457 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1536.00 | −0.0640039 | ||||||||
\(833\) | 20274.0 | 0.843280 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15408.0 | 0.638582 | ||||||||
\(836\) | −608.000 | −0.0251533 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25104.0 | 1.03485 | ||||||||
\(839\) | −8436.00 | −0.347131 | −0.173566 | − | 0.984822i | \(-0.555529\pi\) | ||||
−0.173566 | + | 0.984822i | \(0.555529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | 26240.0 | 1.07398 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7472.00 | −0.304736 | ||||||||
\(845\) | 19452.0 | 0.791916 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5068.00 | −0.205594 | ||||||||
\(848\) | 5792.00 | 0.234550 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2356.00 | −0.0950707 | ||||||||
\(851\) | 57424.0 | 2.31312 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4818.00 | −0.193394 | −0.0966971 | − | 0.995314i | \(-0.530828\pi\) | ||||
−0.0966971 | + | 0.995314i | \(0.530828\pi\) | |||||||
\(854\) | 1072.00 | 0.0429544 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7520.00 | −0.300267 | ||||||||
\(857\) | −29346.0 | −1.16971 | −0.584854 | − | 0.811138i | \(-0.698848\pi\) | ||||
−0.584854 | + | 0.811138i | \(0.698848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45532.0 | 1.80854 | 0.904268 | − | 0.426966i | \(-0.140418\pi\) | ||||
0.904268 | + | 0.426966i | \(0.140418\pi\) | |||||||
\(860\) | 2880.00 | 0.114194 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24776.0 | −0.978972 | ||||||||
\(863\) | −18124.0 | −0.714888 | −0.357444 | − | 0.933935i | \(-0.616352\pi\) | ||||
−0.357444 | + | 0.933935i | \(0.616352\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49608.0 | −1.94997 | ||||||||
\(866\) | 14364.0 | 0.563636 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 288.000 | 0.0112619 | ||||||||
\(869\) | −8624.00 | −0.336650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5760.00 | 0.224076 | ||||||||
\(872\) | −7136.00 | −0.277128 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7372.00 | −0.285311 | ||||||||
\(875\) | 5088.00 | 0.196578 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2824.00 | −0.108734 | −0.0543670 | − | 0.998521i | \(-0.517314\pi\) | ||||
−0.0543670 | + | 0.998521i | \(0.517314\pi\) | |||||||
\(878\) | 32180.0 | 1.23693 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1536.00 | 0.0588393 | ||||||||
\(881\) | −45906.0 | −1.75552 | −0.877760 | − | 0.479101i | \(-0.840963\pi\) | ||||
−0.877760 | + | 0.479101i | \(0.840963\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32292.0 | −1.23070 | −0.615352 | − | 0.788252i | \(-0.710986\pi\) | ||||
−0.615352 | + | 0.788252i | \(0.710986\pi\) | |||||||
\(884\) | 5952.00 | 0.226456 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5088.00 | 0.192929 | ||||||||
\(887\) | −2364.00 | −0.0894874 | −0.0447437 | − | 0.998998i | \(-0.514247\pi\) | ||||
−0.0447437 | + | 0.998998i | \(0.514247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1288.00 | 0.0485918 | ||||||||
\(890\) | 4080.00 | 0.153665 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15960.0 | −0.599081 | ||||||||
\(893\) | 4294.00 | 0.160911 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31920.0 | 1.19214 | ||||||||
\(896\) | 512.000 | 0.0190901 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8676.00 | −0.322407 | ||||||||
\(899\) | −1836.00 | −0.0681135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22444.0 | −0.829876 | ||||||||
\(902\) | 2144.00 | 0.0791434 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14864.0 | 0.546869 | ||||||||
\(905\) | −28080.0 | −1.03139 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4304.00 | −0.157566 | −0.0787828 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787828 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(908\) | 14384.0 | 0.525716 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2304.00 | 0.0839306 | ||||||||
\(911\) | 15060.0 | 0.547706 | 0.273853 | − | 0.961772i | \(-0.411702\pi\) | ||||
0.273853 | + | 0.961772i | \(0.411702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7520.00 | 0.272591 | ||||||||
\(914\) | 20548.0 | 0.743619 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22072.0 | 0.796157 | ||||||||
\(917\) | 6000.00 | 0.216071 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39160.0 | 1.40562 | 0.702812 | − | 0.711375i | \(-0.251927\pi\) | ||||
0.702812 | + | 0.711375i | \(0.251927\pi\) | |||||||
\(920\) | 18624.0 | 0.667408 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1536.00 | −0.0548649 | ||||||||
\(923\) | −19200.0 | −0.684697 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5624.00 | −0.199909 | ||||||||
\(926\) | −22296.0 | −0.791244 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3264.00 | −0.115459 | ||||||||
\(929\) | 33810.0 | 1.19405 | 0.597024 | − | 0.802224i | \(-0.296350\pi\) | ||||
0.597024 | + | 0.802224i | \(0.296350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6213.00 | −0.218714 | ||||||||
\(932\) | −552.000 | −0.0194006 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37064.0 | −1.29847 | ||||||||
\(935\) | −5952.00 | −0.208183 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54614.0 | 1.90412 | 0.952061 | − | 0.305909i | \(-0.0989605\pi\) | ||||
0.952061 | + | 0.305909i | \(0.0989605\pi\) | |||||||
\(938\) | −1920.00 | −0.0668339 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10848.0 | −0.376407 | ||||||||
\(941\) | −11594.0 | −0.401651 | −0.200826 | − | 0.979627i | \(-0.564362\pi\) | ||||
−0.200826 | + | 0.979627i | \(0.564362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25996.0 | 0.897716 | ||||||||
\(944\) | 5056.00 | 0.174321 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 960.000 | 0.0329940 | ||||||||
\(947\) | −9452.00 | −0.324339 | −0.162169 | − | 0.986763i | \(-0.551849\pi\) | ||||
−0.162169 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13872.0 | 0.474504 | ||||||||
\(950\) | 722.000 | 0.0246577 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1984.00 | −0.0675439 | ||||||||
\(953\) | −36966.0 | −1.25650 | −0.628251 | − | 0.778011i | \(-0.716229\pi\) | ||||
−0.628251 | + | 0.778011i | \(0.716229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45816.0 | 1.55243 | ||||||||
\(956\) | −27480.0 | −0.929672 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13884.0 | 0.468238 | ||||||||
\(959\) | 4584.00 | 0.154354 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29467.0 | −0.989124 | ||||||||
\(962\) | 14208.0 | 0.476179 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23320.0 | 0.779136 | ||||||||
\(965\) | 15960.0 | 0.532405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −324.000 | −0.0107747 | −0.00538735 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538735 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(968\) | −10136.0 | −0.336553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4944.00 | −0.163652 | ||||||||
\(971\) | −9084.00 | −0.300226 | −0.150113 | − | 0.988669i | \(-0.547964\pi\) | ||||
−0.150113 | + | 0.988669i | \(0.547964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5456.00 | 0.179765 | ||||||||
\(974\) | −18740.0 | −0.616497 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2144.00 | 0.0703153 | ||||||||
\(977\) | −38142.0 | −1.24900 | −0.624499 | − | 0.781026i | \(-0.714697\pi\) | ||||
−0.624499 | + | 0.781026i | \(0.714697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1360.00 | 0.0443981 | ||||||||
\(980\) | 15696.0 | 0.511623 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27144.0 | 0.882077 | ||||||||
\(983\) | −19248.0 | −0.624533 | −0.312266 | − | 0.949995i | \(-0.601088\pi\) | ||||
−0.312266 | + | 0.949995i | \(0.601088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29184.0 | 0.944040 | ||||||||
\(986\) | 12648.0 | 0.408514 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1824.00 | −0.0587340 | ||||||||
\(989\) | 11640.0 | 0.374247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34070.0 | −1.09210 | −0.546049 | − | 0.837753i | \(-0.683869\pi\) | ||||
−0.546049 | + | 0.837753i | \(0.683869\pi\) | |||||||
\(992\) | 576.000 | 0.0184355 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6400.00 | 0.204221 | ||||||||
\(995\) | −45456.0 | −1.44829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26282.0 | 0.834864 | 0.417432 | − | 0.908708i | \(-0.362930\pi\) | ||||
0.417432 | + | 0.908708i | \(0.362930\pi\) | |||||||
\(998\) | −248.000 | −0.00786603 | ||||||||
\(999\) | 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 | 342.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 114.4.a.c.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 912.4.a.d.1.1 | 1 | |||
57.56 | even | 2 | 2166.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
342.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
912.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
2166.4.a.g.1.1 | 1 | 57.56 | even | 2 |