Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(42.4813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.0000 | −1.83583 | −0.917914 | − | 0.396780i | \(-0.870128\pi\) | ||||
−0.917914 | + | 0.396780i | \(0.870128\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.0000 | −0.493382 | −0.246691 | − | 0.969094i | \(-0.579343\pi\) | ||||
−0.246691 | + | 0.969094i | \(0.579343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −106.000 | −1.51228 | −0.756140 | − | 0.654409i | \(-0.772917\pi\) | ||||
−0.756140 | + | 0.654409i | \(0.772917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44.0000 | 0.531279 | 0.265639 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −56.0000 | −0.507687 | −0.253844 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253844 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 270.000 | 1.72889 | 0.864444 | − | 0.502729i | \(-0.167671\pi\) | ||||
0.864444 | + | 0.502729i | \(0.167671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −204.000 | −1.18192 | −0.590959 | − | 0.806701i | \(-0.701251\pi\) | ||||
−0.590959 | + | 0.806701i | \(0.701251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 170.000 | 0.821007 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 120.000 | 0.533186 | 0.266593 | − | 0.963809i | \(-0.414102\pi\) | ||||
0.266593 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 80.0000 | 0.304729 | 0.152365 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152365 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −536.000 | −1.90091 | −0.950456 | − | 0.310858i | \(-0.899383\pi\) | ||||
−0.950456 | + | 0.310858i | \(0.899383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 536.000 | 1.66348 | 0.831741 | − | 0.555164i | \(-0.187345\pi\) | ||||
0.831741 | + | 0.555164i | \(0.187345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 813.000 | 2.37026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 542.000 | 1.40471 | 0.702353 | − | 0.711829i | \(-0.252133\pi\) | ||||
0.702353 | + | 0.711829i | \(0.252133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 90.0000 | 0.220647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 174.000 | 0.383947 | 0.191973 | − | 0.981400i | \(-0.438511\pi\) | ||||
0.191973 | + | 0.981400i | \(0.438511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 186.000 | 0.390408 | 0.195204 | − | 0.980763i | \(-0.437463\pi\) | ||||
0.195204 | + | 0.980763i | \(0.437463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −60.0000 | −0.114494 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −332.000 | −0.605377 | −0.302688 | − | 0.953090i | \(-0.597884\pi\) | ||||
−0.302688 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 132.000 | 0.220641 | 0.110321 | − | 0.993896i | \(-0.464812\pi\) | ||||
0.110321 | + | 0.993896i | \(0.464812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −602.000 | −0.965189 | −0.482594 | − | 0.875844i | \(-0.660305\pi\) | ||||
−0.482594 | + | 0.875844i | \(0.660305\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 612.000 | 0.905765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 548.000 | 0.780441 | 0.390220 | − | 0.920721i | \(-0.372399\pi\) | ||||
0.390220 | + | 0.920721i | \(0.372399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 492.000 | 0.650651 | 0.325325 | − | 0.945602i | \(-0.394526\pi\) | ||||
0.325325 | + | 0.945602i | \(0.394526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 530.000 | 0.676313 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1052.00 | −1.25294 | −0.626471 | − | 0.779445i | \(-0.715501\pi\) | ||||
−0.626471 | + | 0.779445i | \(0.715501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −408.000 | −0.470000 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −220.000 | −0.237595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 482.000 | 0.504533 | 0.252266 | − | 0.967658i | \(-0.418824\pi\) | ||||
0.252266 | + | 0.967658i | \(0.418824\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1214.00 | 1.19601 | 0.598007 | − | 0.801491i | \(-0.295959\pi\) | ||||
0.598007 | + | 0.801491i | \(0.295959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −898.000 | −0.859054 | −0.429527 | − | 0.903054i | \(-0.641320\pi\) | ||||
−0.429527 | + | 0.903054i | \(0.641320\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1364.00 | −1.23236 | −0.616182 | − | 0.787604i | \(-0.711321\pi\) | ||||
−0.616182 | + | 0.787604i | \(0.711321\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 218.000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1386.00 | 1.15384 | 0.576920 | − | 0.816801i | \(-0.304254\pi\) | ||||
0.576920 | + | 0.816801i | \(0.304254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 280.000 | 0.227045 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3604.00 | 2.77629 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1007.00 | −0.756574 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 814.000 | 0.568747 | 0.284373 | − | 0.958714i | \(-0.408214\pi\) | ||||
0.284373 | + | 0.958714i | \(0.408214\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1282.00 | 0.855029 | 0.427515 | − | 0.904008i | \(-0.359389\pi\) | ||||
0.427515 | + | 0.904008i | \(0.359389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1496.00 | −0.975336 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3066.00 | 1.91202 | 0.956008 | − | 0.293342i | \(-0.0947675\pi\) | ||||
0.956008 | + | 0.293342i | \(0.0947675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1332.00 | 0.812797 | 0.406398 | − | 0.913696i | \(-0.366784\pi\) | ||||
0.406398 | + | 0.913696i | \(0.366784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −216.000 | −0.126313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1350.00 | −0.773182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1470.00 | −0.808236 | −0.404118 | − | 0.914707i | \(-0.632421\pi\) | ||||
−0.404118 | + | 0.914707i | \(0.632421\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2592.00 | 1.39691 | 0.698457 | − | 0.715652i | \(-0.253870\pi\) | ||||
0.698457 | + | 0.715652i | \(0.253870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1020.00 | 0.528570 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3332.00 | −1.69377 | −0.846887 | − | 0.531773i | \(-0.821526\pi\) | ||||
−0.846887 | + | 0.531773i | \(0.821526\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1904.00 | 0.932026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 748.000 | 0.359435 | 0.179717 | − | 0.983718i | \(-0.442482\pi\) | ||||
0.179717 | + | 0.983718i | \(0.442482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2560.00 | 1.18622 | 0.593110 | − | 0.805121i | \(-0.297900\pi\) | ||||
0.593110 | + | 0.805121i | \(0.297900\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1206.00 | 0.530003 | 0.265001 | − | 0.964248i | \(-0.414628\pi\) | ||||
0.265001 | + | 0.964248i | \(0.414628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −850.000 | −0.367165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1694.00 | 0.707349 | 0.353675 | − | 0.935369i | \(-0.384932\pi\) | ||||
0.353675 | + | 0.935369i | \(0.384932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3722.00 | 1.52848 | 0.764238 | − | 0.644935i | \(-0.223115\pi\) | ||||
0.764238 | + | 0.644935i | \(0.223115\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −600.000 | −0.238448 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1908.00 | 0.746133 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2836.00 | −1.07438 | −0.537188 | − | 0.843463i | \(-0.680513\pi\) | ||||
−0.537188 | + | 0.843463i | \(0.680513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −234.000 | −0.0872730 | −0.0436365 | − | 0.999047i | \(-0.513894\pi\) | ||||
−0.0436365 | + | 0.999047i | \(0.513894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3814.00 | −1.37937 | −0.689686 | − | 0.724109i | \(-0.742251\pi\) | ||||
−0.689686 | + | 0.724109i | \(0.742251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2352.00 | −0.837833 | −0.418917 | − | 0.908025i | \(-0.637590\pi\) | ||||
−0.418917 | + | 0.908025i | \(0.637590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9180.00 | −3.17394 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −400.000 | −0.136279 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −792.000 | −0.262123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3660.00 | 1.19415 | 0.597073 | − | 0.802187i | \(-0.296330\pi\) | ||||
0.597073 | + | 0.802187i | \(0.296330\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2680.00 | 0.850114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6936.00 | 2.16980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1272.00 | −0.387167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2646.00 | 0.794571 | 0.397285 | − | 0.917695i | \(-0.369952\pi\) | ||||
0.397285 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −240.000 | −0.0701734 | −0.0350867 | − | 0.999384i | \(-0.511171\pi\) | ||||
−0.0350867 | + | 0.999384i | \(0.511171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4698.00 | −1.35569 | −0.677844 | − | 0.735206i | \(-0.737086\pi\) | ||||
−0.677844 | + | 0.735206i | \(0.737086\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3814.00 | 1.07238 | 0.536188 | − | 0.844099i | \(-0.319864\pi\) | ||||
0.536188 | + | 0.844099i | \(0.319864\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2680.00 | −0.743932 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2148.00 | 0.581350 | 0.290675 | − | 0.956822i | \(-0.406120\pi\) | ||||
0.290675 | + | 0.956822i | \(0.406120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3370.00 | −0.900750 | −0.450375 | − | 0.892839i | \(-0.648710\pi\) | ||||
−0.450375 | + | 0.892839i | \(0.648710\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4065.00 | −1.06001 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 528.000 | 0.136016 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6134.00 | −1.54253 | −0.771264 | − | 0.636515i | \(-0.780375\pi\) | ||||
−0.771264 | + | 0.636515i | \(0.780375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1008.00 | 0.250484 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4566.00 | −1.10825 | −0.554123 | − | 0.832435i | \(-0.686946\pi\) | ||||
−0.554123 | + | 0.832435i | \(0.686946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4080.00 | −0.978837 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1920.00 | 0.450161 | 0.225080 | − | 0.974340i | \(-0.427736\pi\) | ||||
0.225080 | + | 0.974340i | \(0.427736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2710.00 | −0.628204 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5802.00 | −1.31507 | −0.657536 | − | 0.753423i | \(-0.728401\pi\) | ||||
−0.657536 | + | 0.753423i | \(0.728401\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1640.00 | −0.367612 | −0.183806 | − | 0.982963i | \(-0.558842\pi\) | ||||
−0.183806 | + | 0.982963i | \(0.558842\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −450.000 | −0.0986764 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2792.00 | −0.605614 | −0.302807 | − | 0.953052i | \(-0.597924\pi\) | ||||
−0.302807 | + | 0.953052i | \(0.597924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1108.00 | 0.235223 | 0.117612 | − | 0.993060i | \(-0.462476\pi\) | ||||
0.117612 | + | 0.993060i | \(0.462476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6028.00 | −1.26617 | −0.633087 | − | 0.774080i | \(-0.718213\pi\) | ||||
−0.633087 | + | 0.774080i | \(0.718213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2720.00 | −0.559430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6323.00 | 1.28699 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7994.00 | 1.59391 | 0.796953 | − | 0.604041i | \(-0.206444\pi\) | ||||
0.796953 | + | 0.604041i | \(0.206444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −870.000 | −0.171706 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −672.000 | −0.129976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18224.0 | 3.48975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −930.000 | −0.174596 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −736.000 | −0.136827 | −0.0684133 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684133 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5380.00 | 0.980938 | 0.490469 | − | 0.871459i | \(-0.336825\pi\) | ||||
0.490469 | + | 0.871459i | \(0.336825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1370.00 | −0.247402 | −0.123701 | − | 0.992320i | \(-0.539476\pi\) | ||||
−0.123701 | + | 0.992320i | \(0.539476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5770.00 | 1.02232 | 0.511160 | − | 0.859486i | \(-0.329216\pi\) | ||||
0.511160 | + | 0.859486i | \(0.329216\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4860.00 | −0.853002 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4664.00 | −0.803442 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 300.000 | 0.0512031 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18224.0 | −3.05387 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4172.00 | 0.692791 | 0.346396 | − | 0.938089i | \(-0.387406\pi\) | ||||
0.346396 | + | 0.938089i | \(0.387406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1660.00 | 0.270733 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8206.00 | 1.32644 | 0.663219 | − | 0.748426i | \(-0.269190\pi\) | ||||
0.663219 | + | 0.748426i | \(0.269190\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3672.00 | 0.583138 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15980.0 | −2.51557 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10848.0 | −1.67825 | −0.839123 | − | 0.543942i | \(-0.816931\pi\) | ||||
−0.839123 | + | 0.543942i | \(0.816931\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1694.00 | −0.259822 | −0.129911 | − | 0.991526i | \(-0.541469\pi\) | ||||
−0.129911 | + | 0.991526i | \(0.541469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6642.00 | −1.00147 | −0.500734 | − | 0.865601i | \(-0.666936\pi\) | ||||
−0.500734 | + | 0.865601i | \(0.666936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −660.000 | −0.0986737 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10376.0 | 1.52542 | 0.762708 | − | 0.646743i | \(-0.223869\pi\) | ||||
0.762708 | + | 0.646743i | \(0.223869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3010.00 | 0.431645 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2198.00 | 0.312629 | 0.156314 | − | 0.987707i | \(-0.450039\pi\) | ||||
0.156314 | + | 0.987707i | \(0.450039\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18428.0 | −2.57880 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12220.0 | −1.69632 | −0.848160 | − | 0.529740i | \(-0.822290\pi\) | ||||
−0.848160 | + | 0.529740i | \(0.822290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3240.00 | 0.442622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10388.0 | 1.40790 | 0.703952 | − | 0.710247i | \(-0.251417\pi\) | ||||
0.703952 | + | 0.710247i | \(0.251417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10552.0 | −1.40779 | −0.703893 | − | 0.710306i | \(-0.748557\pi\) | ||||
−0.703893 | + | 0.710306i | \(0.748557\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3060.00 | −0.405070 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8262.00 | −1.07686 | −0.538432 | − | 0.842669i | \(-0.680983\pi\) | ||||
−0.538432 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5936.00 | 0.767766 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2740.00 | −0.349024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2864.00 | 0.362066 | 0.181033 | − | 0.983477i | \(-0.442056\pi\) | ||||
0.181033 | + | 0.983477i | \(0.442056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12588.0 | −1.56762 | −0.783809 | − | 0.621002i | \(-0.786726\pi\) | ||||
−0.783809 | + | 0.621002i | \(0.786726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2448.00 | −0.302589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2160.00 | −0.263064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10330.0 | 1.24886 | 0.624432 | − | 0.781079i | \(-0.285330\pi\) | ||||
0.624432 | + | 0.781079i | \(0.285330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5916.00 | −0.704860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2460.00 | −0.290980 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1250.00 | 0.145743 | 0.0728717 | − | 0.997341i | \(-0.476784\pi\) | ||||
0.0728717 | + | 0.997341i | \(0.476784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5670.00 | 0.656387 | 0.328193 | − | 0.944611i | \(-0.393560\pi\) | ||||
0.328193 | + | 0.944611i | \(0.393560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2650.00 | −0.302456 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6324.00 | −0.716721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12976.0 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9050.00 | −1.00442 | −0.502212 | − | 0.864745i | \(-0.667480\pi\) | ||||
−0.502212 | + | 0.864745i | \(0.667480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2464.00 | −0.269723 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17528.0 | 1.90562 | 0.952808 | − | 0.303572i | \(-0.0981794\pi\) | ||||
0.952808 | + | 0.303572i | \(0.0981794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2568.00 | −0.275416 | −0.137708 | − | 0.990473i | \(-0.543974\pi\) | ||||
−0.137708 | + | 0.990473i | \(0.543974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5260.00 | 0.560332 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12652.0 | 1.32981 | 0.664905 | − | 0.746928i | \(-0.268472\pi\) | ||||
0.664905 | + | 0.746928i | \(0.268472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1440.00 | −0.150348 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2040.00 | 0.210190 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6230.00 | −0.637696 | −0.318848 | − | 0.947806i | \(-0.603296\pi\) | ||||
−0.318848 | + | 0.947806i | \(0.603296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5290.00 | 0.534447 | 0.267223 | − | 0.963635i | \(-0.413894\pi\) | ||||
0.267223 | + | 0.963635i | \(0.413894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8110.00 | −0.814047 | −0.407023 | − | 0.913418i | \(-0.633433\pi\) | ||||
−0.407023 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2020.00 | 0.200159 | 0.100080 | − | 0.994979i | \(-0.468090\pi\) | ||||
0.100080 | + | 0.994979i | \(0.468090\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11288.0 | 1.11137 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9648.00 | 0.937876 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1100.00 | 0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9684.00 | 0.923744 | 0.461872 | − | 0.886947i | \(-0.347178\pi\) | ||||
0.461872 | + | 0.886947i | \(0.347178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1440.00 | 0.136504 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2410.00 | −0.225634 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18426.0 | 1.71450 | 0.857250 | − | 0.514900i | \(-0.172171\pi\) | ||||
0.857250 | + | 0.514900i | \(0.172171\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4558.00 | −0.418940 | −0.209470 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209470 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28620.0 | −2.61456 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4488.00 | −0.405059 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 460.000 | 0.0412674 | 0.0206337 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206337 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8568.00 | 0.759499 | 0.379750 | − | 0.925089i | \(-0.376010\pi\) | ||||
0.379750 | + | 0.925089i | \(0.376010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6070.00 | −0.534874 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16374.0 | 1.42586 | 0.712932 | − | 0.701233i | \(-0.247367\pi\) | ||||
0.712932 | + | 0.701233i | \(0.247367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20468.0 | 1.77192 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4490.00 | 0.384181 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9648.00 | −0.820732 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21620.0 | 1.81802 | 0.909011 | − | 0.416772i | \(-0.136839\pi\) | ||||
0.909011 | + | 0.416772i | \(0.136839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16524.0 | −1.38154 | −0.690769 | − | 0.723076i | \(-0.742728\pi\) | ||||
−0.690769 | + | 0.723076i | \(0.742728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21624.0 | 1.78739 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9031.00 | −0.742254 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 960.000 | 0.0780154 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6820.00 | 0.551130 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14634.0 | −1.16945 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4990.00 | −0.396556 | −0.198278 | − | 0.980146i | \(-0.563535\pi\) | ||||
−0.198278 | + | 0.980146i | \(0.563535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1090.00 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15224.0 | 1.19000 | 0.595001 | − | 0.803725i | \(-0.297152\pi\) | ||||
0.595001 | + | 0.803725i | \(0.297152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11880.0 | 0.918521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18632.0 | −1.43275 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5698.00 | −0.433451 | −0.216725 | − | 0.976233i | \(-0.569538\pi\) | ||||
−0.216725 | + | 0.976233i | \(0.569538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6432.00 | −0.486663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5976.00 | −0.447351 | −0.223675 | − | 0.974664i | \(-0.571806\pi\) | ||||
−0.223675 | + | 0.974664i | \(0.571806\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6930.00 | −0.516013 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16460.0 | 1.21272 | 0.606361 | − | 0.795189i | \(-0.292629\pi\) | ||||
0.606361 | + | 0.795189i | \(0.292629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18236.0 | 1.33652 | 0.668260 | − | 0.743928i | \(-0.267039\pi\) | ||||
0.668260 | + | 0.743928i | \(0.267039\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1400.00 | −0.101537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20842.0 | 1.50375 | 0.751875 | − | 0.659306i | \(-0.229150\pi\) | ||||
0.751875 | + | 0.659306i | \(0.229150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16728.0 | −1.19448 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9756.00 | −0.693057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11772.0 | 0.827738 | 0.413869 | − | 0.910336i | \(-0.364177\pi\) | ||||
0.413869 | + | 0.910336i | \(0.364177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8976.00 | −0.627928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4514.00 | 0.312593 | 0.156297 | − | 0.987710i | \(-0.450044\pi\) | ||||
0.156297 | + | 0.987710i | \(0.450044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18020.0 | −1.24159 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25096.0 | −1.71184 | −0.855922 | − | 0.517105i | \(-0.827010\pi\) | ||||
−0.855922 | + | 0.517105i | \(0.827010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16262.0 | 1.10373 | 0.551864 | − | 0.833934i | \(-0.313917\pi\) | ||||
0.551864 | + | 0.833934i | \(0.313917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5035.00 | 0.338350 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2262.00 | −0.151255 | −0.0756275 | − | 0.997136i | \(-0.524096\pi\) | ||||
−0.0756275 | + | 0.997136i | \(0.524096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6432.00 | 0.425877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14216.0 | 0.936670 | 0.468335 | − | 0.883551i | \(-0.344854\pi\) | ||||
0.468335 | + | 0.883551i | \(0.344854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2558.00 | 0.166906 | 0.0834532 | − | 0.996512i | \(-0.473405\pi\) | ||||
0.0834532 | + | 0.996512i | \(0.473405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17044.0 | 1.10671 | 0.553357 | − | 0.832944i | \(-0.313346\pi\) | ||||
0.553357 | + | 0.832944i | \(0.313346\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35768.0 | 2.30018 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12720.0 | −0.806327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20980.0 | −1.32361 | −0.661807 | − | 0.749674i | \(-0.730210\pi\) | ||||
−0.661807 | + | 0.749674i | \(0.730210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4070.00 | −0.254351 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9756.00 | 0.606824 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7176.00 | 0.442176 | 0.221088 | − | 0.975254i | \(-0.429039\pi\) | ||||
0.221088 | + | 0.975254i | \(0.429039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2724.00 | 0.167067 | 0.0835335 | − | 0.996505i | \(-0.473379\pi\) | ||||
0.0835335 | + | 0.996505i | \(0.473379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10392.0 | 0.631455 | 0.315728 | − | 0.948850i | \(-0.397751\pi\) | ||||
0.315728 | + | 0.948850i | \(0.397751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3132.00 | −0.189433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11958.0 | −0.716620 | −0.358310 | − | 0.933603i | \(-0.616647\pi\) | ||||
−0.358310 | + | 0.933603i | \(0.616647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6410.00 | −0.382381 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13366.0 | −0.790084 | −0.395042 | − | 0.918663i | \(-0.629270\pi\) | ||||
−0.395042 | + | 0.918663i | \(0.629270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14698.0 | 0.864880 | 0.432440 | − | 0.901663i | \(-0.357653\pi\) | ||||
0.432440 | + | 0.901663i | \(0.357653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7480.00 | 0.436183 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15120.0 | −0.877734 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3348.00 | −0.192620 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7570.00 | −0.433584 | −0.216792 | − | 0.976218i | \(-0.569559\pi\) | ||||
−0.216792 | + | 0.976218i | \(0.569559\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21378.0 | 1.21362 | 0.606812 | − | 0.794845i | \(-0.292448\pi\) | ||||
0.606812 | + | 0.794845i | \(0.292448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16388.0 | −0.926235 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15804.0 | 0.885393 | 0.442696 | − | 0.896672i | \(-0.354022\pi\) | ||||
0.442696 | + | 0.896672i | \(0.354022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15330.0 | −0.855079 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6504.00 | 0.359627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22028.0 | 1.21271 | 0.606356 | − | 0.795193i | \(-0.292630\pi\) | ||||
0.606356 | + | 0.795193i | \(0.292630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6660.00 | −0.363494 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8480.00 | −0.460836 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1762.00 | −0.0949356 | −0.0474678 | − | 0.998873i | \(-0.515115\pi\) | ||||
−0.0474678 | + | 0.998873i | \(0.515115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5280.00 | 0.283270 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41276.0 | −2.19568 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2474.00 | −0.131048 | −0.0655240 | − | 0.997851i | \(-0.520872\pi\) | ||||
−0.0655240 | + | 0.997851i | \(0.520872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11424.0 | 0.600045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1080.00 | 0.0564891 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32040.0 | 1.66188 | 0.830939 | − | 0.556363i | \(-0.187804\pi\) | ||||
0.830939 | + | 0.556363i | \(0.187804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30532.0 | 1.57708 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6750.00 | 0.345778 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12874.0 | 0.656768 | 0.328384 | − | 0.944544i | \(-0.393496\pi\) | ||||
0.328384 | + | 0.944544i | \(0.393496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 56816.0 | 2.87471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28208.0 | 1.42140 | 0.710700 | − | 0.703495i | \(-0.248378\pi\) | ||||
0.710700 | + | 0.703495i | \(0.248378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5976.00 | 0.298682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29068.0 | −1.44693 | −0.723467 | − | 0.690359i | \(-0.757452\pi\) | ||||
−0.723467 | + | 0.690359i | \(0.757452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28152.0 | 1.39004 | 0.695018 | − | 0.718992i | \(-0.255396\pi\) | ||||
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7350.00 | 0.361454 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46376.0 | 2.26241 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29916.0 | 1.45360 | 0.726798 | − | 0.686851i | \(-0.241008\pi\) | ||||
0.726798 | + | 0.686851i | \(0.241008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12960.0 | −0.624719 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32904.0 | 1.57981 | 0.789905 | − | 0.613229i | \(-0.210130\pi\) | ||||
0.789905 | + | 0.613229i | \(0.210130\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21764.0 | −1.03672 | −0.518360 | − | 0.855162i | \(-0.673457\pi\) | ||||
−0.518360 | + | 0.855162i | \(0.673457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7412.00 | −0.351681 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2088.00 | 0.0982964 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3570.00 | −0.167409 | −0.0837045 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837045 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19486.0 | −0.906679 | −0.453339 | − | 0.891338i | \(-0.649767\pi\) | ||||
−0.453339 | + | 0.891338i | \(0.649767\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5100.00 | −0.236384 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3520.00 | 0.161896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2376.00 | −0.108860 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16660.0 | 0.757479 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19764.0 | −0.895185 | −0.447592 | − | 0.894238i | \(-0.647718\pi\) | ||||
−0.447592 | + | 0.894238i | \(0.647718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47124.0 | −2.11825 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2232.00 | 0.0999504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14390.0 | 0.639548 | 0.319774 | − | 0.947494i | \(-0.396393\pi\) | ||||
0.319774 | + | 0.947494i | \(0.396393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56816.0 | −2.51565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10836.0 | 0.476207 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9520.00 | −0.416815 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28536.0 | 1.24014 | 0.620069 | − | 0.784547i | \(-0.287104\pi\) | ||||
0.620069 | + | 0.784547i | \(0.287104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27732.0 | −1.20074 | −0.600371 | − | 0.799721i | \(-0.704981\pi\) | ||||
−0.600371 | + | 0.799721i | \(0.704981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3740.00 | −0.160744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23584.0 | −1.00991 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8086.00 | 0.343731 | 0.171866 | − | 0.985120i | \(-0.445021\pi\) | ||||
0.171866 | + | 0.985120i | \(0.445021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39854.0 | −1.68800 | −0.843999 | − | 0.536344i | \(-0.819805\pi\) | ||||
−0.843999 | + | 0.536344i | \(0.819805\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17752.0 | 0.746430 | 0.373215 | − | 0.927745i | \(-0.378255\pi\) | ||||
0.373215 | + | 0.927745i | \(0.378255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23858.0 | 0.999545 | 0.499772 | − | 0.866157i | \(-0.333417\pi\) | ||||
0.499772 | + | 0.866157i | \(0.333417\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −86178.0 | −3.58450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12800.0 | −0.530494 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13888.0 | −0.571474 | −0.285737 | − | 0.958308i | \(-0.592238\pi\) | ||||
−0.285737 | + | 0.958308i | \(0.592238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48511.0 | 1.98905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10265.0 | 0.417901 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34238.0 | 1.38894 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6720.00 | −0.270692 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16568.0 | −0.665038 | −0.332519 | − | 0.943097i | \(-0.607899\pi\) | ||||
−0.332519 | + | 0.943097i | \(0.607899\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13034.0 | −0.519525 | −0.259763 | − | 0.965673i | \(-0.583644\pi\) | ||||
−0.259763 | + | 0.965673i | \(0.583644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34356.0 | 1.36462 | 0.682312 | − | 0.731061i | \(-0.260975\pi\) | ||||
0.682312 | + | 0.731061i | \(0.260975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16016.0 | −0.631739 | −0.315870 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315870 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6030.00 | −0.237024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9864.00 | −0.385056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3984.00 | −0.154986 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4250.00 | 0.164201 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19780.0 | 0.761600 | 0.380800 | − | 0.924657i | \(-0.375649\pi\) | ||||
0.380800 | + | 0.924657i | \(0.375649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41036.0 | −1.56928 | −0.784641 | − | 0.619950i | \(-0.787153\pi\) | ||||
−0.784641 | + | 0.619950i | \(0.787153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35108.0 | 1.33803 | 0.669014 | − | 0.743250i | \(-0.266717\pi\) | ||||
0.669014 | + | 0.743250i | \(0.266717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18648.0 | −0.705906 | −0.352953 | − | 0.935641i | \(-0.614822\pi\) | ||||
−0.352953 | + | 0.935641i | \(0.614822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27676.0 | −1.04412 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23584.0 | 0.883772 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8470.00 | −0.316336 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55080.0 | −2.04340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57452.0 | −2.12431 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18610.0 | −0.683555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21688.0 | −0.793978 | −0.396989 | − | 0.917823i | \(-0.629945\pi\) | ||||
−0.396989 | + | 0.917823i | \(0.629945\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42064.0 | 1.52979 | 0.764897 | − | 0.644153i | \(-0.222790\pi\) | ||||
0.764897 | + | 0.644153i | \(0.222790\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8856.00 | −0.321020 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43588.0 | −1.56969 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44420.0 | 1.59443 | 0.797215 | − | 0.603696i | \(-0.206306\pi\) | ||||
0.797215 | + | 0.603696i | \(0.206306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1584.00 | 0.0564875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3000.00 | 0.106637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17124.0 | −0.604758 | −0.302379 | − | 0.953188i | \(-0.597781\pi\) | ||||
−0.302379 | + | 0.953188i | \(0.597781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35772.0 | 1.25927 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9540.00 | −0.333681 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11110.0 | −0.387351 | −0.193675 | − | 0.981066i | \(-0.562041\pi\) | ||||
−0.193675 | + | 0.981066i | \(0.562041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12962.0 | 0.449043 | 0.224521 | − | 0.974469i | \(-0.427918\pi\) | ||||
0.224521 | + | 0.974469i | \(0.427918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4480.00 | −0.154707 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25672.0 | 0.880916 | 0.440458 | − | 0.897773i | \(-0.354816\pi\) | ||||
0.440458 | + | 0.897773i | \(0.354816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7224.00 | −0.247103 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2082.00 | 0.0707687 | 0.0353844 | − | 0.999374i | \(-0.488734\pi\) | ||||
0.0353844 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14180.0 | 0.480475 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −104244. | −3.51013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11825.0 | 0.396932 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1170.00 | 0.0390297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5666.00 | −0.188424 | −0.0942121 | − | 0.995552i | \(-0.530033\pi\) | ||||
−0.0942121 | + | 0.995552i | \(0.530033\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28622.0 | −0.945956 | −0.472978 | − | 0.881074i | \(-0.656821\pi\) | ||||
−0.472978 | + | 0.881074i | \(0.656821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45288.0 | −1.49215 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24586.0 | −0.805093 | −0.402546 | − | 0.915400i | \(-0.631875\pi\) | ||||
−0.402546 | + | 0.915400i | \(0.631875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18936.0 | 0.618179 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40632.0 | −1.31837 | −0.659186 | − | 0.751980i | \(-0.729099\pi\) | ||||
−0.659186 | + | 0.751980i | \(0.729099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19070.0 | 0.616874 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30016.0 | 0.965069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8768.00 | −0.281054 | −0.140527 | − | 0.990077i | \(-0.544880\pi\) | ||||
−0.140527 | + | 0.990077i | \(0.544880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11760.0 | 0.374691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37212.0 | 1.18206 | 0.591031 | − | 0.806649i | \(-0.298721\pi\) | ||||
0.591031 | + | 0.806649i | \(0.298721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 720.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 720.4.a.p.1.1 | 1 | |||
4.3 | odd | 2 | 360.4.a.g.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 360.4.a.o.1.1 | yes | 1 | ||
20.3 | even | 4 | 1800.4.f.o.649.1 | 2 | |||
20.7 | even | 4 | 1800.4.f.o.649.2 | 2 | |||
20.19 | odd | 2 | 1800.4.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.f.i.649.1 | 2 | |||
60.47 | odd | 4 | 1800.4.f.i.649.2 | 2 | |||
60.59 | even | 2 | 1800.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.a.g.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
360.4.a.o.1.1 | yes | 1 | 12.11 | even | 2 | ||
720.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
720.4.a.p.1.1 | 1 | 3.2 | odd | 2 | |||
1800.4.a.a.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
1800.4.f.i.649.1 | 2 | 60.23 | odd | 4 | |||
1800.4.f.i.649.2 | 2 | 60.47 | odd | 4 | |||
1800.4.f.o.649.1 | 2 | 20.3 | even | 4 | |||
1800.4.f.o.649.2 | 2 | 20.7 | even | 4 |