Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −6.08276 | −1.17063 | −0.585314 | − | 0.810807i | \(-0.699029\pi\) | ||||
−0.585314 | + | 0.810807i | \(0.699029\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.16553 | −0.462019 | −0.231009 | − | 0.972952i | \(-0.574203\pi\) | ||||
−0.231009 | + | 0.972952i | \(0.574203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.0000 | 0.370370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.5793 | −1.60567 | −0.802833 | − | 0.596203i | \(-0.796675\pi\) | ||||
−0.802833 | + | 0.596203i | \(0.796675\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.3311 | 0.817779 | 0.408889 | − | 0.912584i | \(-0.365916\pi\) | ||||
0.408889 | + | 0.912584i | \(0.365916\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 31.4207 | 0.540852 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 52.6689 | 0.751417 | 0.375709 | − | 0.926738i | \(-0.377399\pi\) | ||||
0.375709 | + | 0.926738i | \(0.377399\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −130.248 | −1.57268 | −0.786342 | − | 0.617791i | \(-0.788028\pi\) | ||||
−0.786342 | + | 0.617791i | \(0.788028\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −76.5793 | −0.694256 | −0.347128 | − | 0.937818i | \(-0.612843\pi\) | ||||
−0.347128 | + | 0.937818i | \(0.612843\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.3174 | −0.786539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 103.407 | 0.737062 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −288.317 | −1.84618 | −0.923089 | − | 0.384585i | \(-0.874344\pi\) | ||||
−0.923089 | + | 0.384585i | \(0.874344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −140.579 | −0.814477 | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 356.324 | 1.87964 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −82.4760 | −0.366459 | −0.183229 | − | 0.983070i | \(-0.558655\pi\) | ||||
−0.183229 | + | 0.983070i | \(0.558655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −233.159 | −0.957315 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 282.993 | 1.07795 | 0.538977 | − | 0.842321i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842321i | \(0.318811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 172.000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −51.6553 | −0.171118 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 133.241 | 0.413516 | 0.206758 | − | 0.978392i | \(-0.433709\pi\) | ||||
0.206758 | + | 0.978392i | \(0.433709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −320.373 | −0.879630 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.4760 | 0.0945352 | 0.0472676 | − | 0.998882i | \(-0.484949\pi\) | ||||
0.0472676 | + | 0.998882i | \(0.484949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 302.593 | 0.741848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 792.269 | 1.84103 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −253.062 | −0.558405 | −0.279202 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279202 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −499.124 | −1.04764 | −0.523822 | − | 0.851827i | \(-0.675494\pi\) | ||||
−0.523822 | + | 0.851827i | \(0.675494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −198.000 | −0.377829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −210.579 | −0.383976 | −0.191988 | − | 0.981397i | \(-0.561493\pi\) | ||||
−0.191988 | + | 0.981397i | \(0.561493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 465.814 | 0.812716 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −107.365 | −0.179464 | −0.0897318 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897318 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −361.345 | −0.579345 | −0.289673 | − | 0.957126i | \(-0.593546\pi\) | ||||
−0.289673 | + | 0.957126i | \(0.593546\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 598.041 | 0.920745 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 835.007 | 1.18919 | 0.594593 | − | 0.804027i | \(-0.297313\pi\) | ||||
0.594593 | + | 0.804027i | \(0.297313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −899.000 | −1.23320 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 731.283 | 0.967093 | 0.483547 | − | 0.875319i | \(-0.339348\pi\) | ||||
0.483547 | + | 0.875319i | \(0.339348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −272.063 | −0.347169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1753.77 | 2.16119 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 217.966 | 0.259599 | 0.129800 | − | 0.991540i | \(-0.458567\pi\) | ||||
0.129800 | + | 0.991540i | \(0.458567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 855.111 | 0.953450 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 672.801 | 0.726610 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −252.290 | −0.264084 | −0.132042 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132042 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −585.793 | −0.594691 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1155.77 | 1.13865 | 0.569325 | − | 0.822112i | \(-0.307205\pi\) | ||||
0.569325 | + | 0.822112i | \(0.307205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1051.26 | 1.00566 | 0.502831 | − | 0.864385i | \(-0.332292\pi\) | ||||
0.502831 | + | 0.864385i | \(0.332292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2075.21 | 1.87494 | 0.937470 | − | 0.348067i | \(-0.113162\pi\) | ||||
0.937470 | + | 0.348067i | \(0.113162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1216.16 | −1.06869 | −0.534343 | − | 0.845267i | \(-0.679441\pi\) | ||||
−0.534343 | + | 0.845267i | \(0.679441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 501.682 | 0.428987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1585.59 | 1.32000 | 0.659998 | − | 0.751268i | \(-0.270557\pi\) | ||||
0.659998 | + | 0.751268i | \(0.270557\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 395.572 | 0.320759 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 383.311 | 0.302881 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2100.54 | 1.57817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1721.38 | −1.26188 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1153.55 | 0.825414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1107.37 | 0.773723 | 0.386861 | − | 0.922138i | \(-0.373559\pi\) | ||||
0.386861 | + | 0.922138i | \(0.373559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1046.24 | −0.714077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 885.284 | 0.590440 | 0.295220 | − | 0.955429i | \(-0.404607\pi\) | ||||
0.295220 | + | 0.955429i | \(0.404607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −534.151 | −0.340536 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2153.54 | 1.34299 | 0.671494 | − | 0.741010i | \(-0.265653\pi\) | ||||
0.671494 | + | 0.741010i | \(0.265653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −672.580 | −0.410414 | −0.205207 | − | 0.978719i | \(-0.565787\pi\) | ||||
−0.205207 | + | 0.978719i | \(0.565787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −810.476 | −0.484074 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2245.41 | −1.31308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1489.31 | 0.852969 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1803.33 | −0.991508 | −0.495754 | − | 0.868463i | \(-0.665108\pi\) | ||||
−0.495754 | + | 0.868463i | \(0.665108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1115.01 | −0.600914 | −0.300457 | − | 0.953795i | \(-0.597139\pi\) | ||||
−0.300457 | + | 0.953795i | \(0.597139\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 526.689 | 0.278303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 726.166 | 0.376304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1678.31 | 0.853146 | 0.426573 | − | 0.904453i | \(-0.359721\pi\) | ||||
0.426573 | + | 0.904453i | \(0.359721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −221.875 | −0.110666 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1584.59 | −0.761442 | −0.380721 | − | 0.924690i | \(-0.624324\pi\) | ||||
−0.380721 | + | 0.924690i | \(0.624324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1840.60 | −0.868428 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 619.669 | 0.287134 | 0.143567 | − | 0.989641i | \(-0.454143\pi\) | ||||
0.143567 | + | 0.989641i | \(0.454143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −727.731 | −0.331238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1302.48 | −0.582476 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3580.77 | 1.57365 | 0.786823 | − | 0.617179i | \(-0.211725\pi\) | ||||
0.786823 | + | 0.617179i | \(0.211725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1539.32 | 0.653685 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 575.546 | 0.240326 | 0.120163 | − | 0.992754i | \(-0.461658\pi\) | ||||
0.120163 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1556.51 | −0.639197 | −0.319598 | − | 0.947553i | \(-0.603548\pi\) | ||||
−0.319598 | + | 0.947553i | \(0.603548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3036.06 | 1.22640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 426.032 | 0.169311 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3085.31 | −1.20653 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −799.118 | −0.302734 | −0.151367 | − | 0.988478i | \(-0.548367\pi\) | ||||
−0.151367 | + | 0.988478i | \(0.548367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −558.048 | −0.208130 | −0.104065 | − | 0.994570i | \(-0.533185\pi\) | ||||
−0.104065 | + | 0.994570i | \(0.533185\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1204.39 | 0.442297 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1729.59 | −0.625523 | −0.312761 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312761 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4285.55 | 1.52660 | 0.763302 | − | 0.646041i | \(-0.223577\pi\) | ||||
0.763302 | + | 0.646041i | \(0.223577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1280.90 | 0.449493 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1461.81 | −0.498035 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −765.793 | −0.257132 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7629.86 | 2.52521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −849.904 | −0.277298 | −0.138649 | − | 0.990342i | \(-0.544276\pi\) | ||||
−0.138649 | + | 0.990342i | \(0.544276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 653.078 | 0.210085 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −888.470 | −0.281829 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2197.97 | 0.678198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2018.86 | 0.614493 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4377.66 | 1.31457 | 0.657286 | − | 0.753641i | \(-0.271704\pi\) | ||||
0.657286 | + | 0.753641i | \(0.271704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −983.174 | −0.291311 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5119.66 | −1.49693 | −0.748466 | − | 0.663173i | \(-0.769209\pi\) | ||||
−0.748466 | + | 0.663173i | \(0.769209\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5881.31 | −1.69715 | −0.848576 | − | 0.529074i | \(-0.822539\pi\) | ||||
−0.848576 | + | 0.529074i | \(0.822539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 212.078 | 0.0596295 | 0.0298147 | − | 0.999555i | \(-0.490508\pi\) | ||||
0.0298147 | + | 0.999555i | \(0.490508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −688.262 | −0.191052 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5079.15 | −1.39209 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5202.95 | −1.40816 | −0.704082 | − | 0.710119i | \(-0.748641\pi\) | ||||
−0.704082 | + | 0.710119i | \(0.748641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2837.12 | −0.758320 | −0.379160 | − | 0.925331i | \(-0.623787\pi\) | ||||
−0.379160 | + | 0.925331i | \(0.623787\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2676.42 | 0.706552 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4992.55 | −1.28611 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4448.22 | −1.13211 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4697.05 | −1.18118 | −0.590588 | − | 0.806973i | \(-0.701104\pi\) | ||||
−0.590588 | + | 0.806973i | \(0.701104\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4485.97 | 1.11474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1654.89 | 0.406406 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7003.72 | −1.69992 | −0.849961 | − | 0.526845i | \(-0.823375\pi\) | ||||
−0.849961 | + | 0.526845i | \(0.823375\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2883.17 | −0.683770 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1228.31 | −0.287987 | −0.143994 | − | 0.989579i | \(-0.545994\pi\) | ||||
−0.143994 | + | 0.989579i | \(0.545994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −188.418 | −0.0436770 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1325.83 | −0.303894 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −141.885 | −0.0321593 | −0.0160797 | − | 0.999871i | \(-0.505119\pi\) | ||||
−0.0160797 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −364.775 | −0.0817656 | −0.0408828 | − | 0.999164i | \(-0.513017\pi\) | ||||
−0.0408828 | + | 0.999164i | \(0.513017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5759.37 | 1.26292 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1988.48 | 0.431321 | 0.215661 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215661 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1405.79 | −0.301658 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4903.93 | 1.04108 | 0.520541 | − | 0.853837i | \(-0.325730\pi\) | ||||
0.520541 | + | 0.853837i | \(0.325730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3260.07 | 0.684775 | 0.342387 | − | 0.939559i | \(-0.388765\pi\) | ||||
0.342387 | + | 0.939559i | \(0.388765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4092.49 | −0.850590 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2138.98 | −0.435372 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1534.62 | 0.309144 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1613.67 | −0.321746 | −0.160873 | − | 0.986975i | \(-0.551431\pi\) | ||||
−0.160873 | + | 0.986975i | \(0.551431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1307.20 | 0.257993 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6057.51 | −1.18348 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2935.37 | −0.567748 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7030.29 | −1.33294 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2578.24 | 0.484031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2846.16 | −0.529116 | −0.264558 | − | 0.964370i | \(-0.585226\pi\) | ||||
−0.264558 | + | 0.964370i | \(0.585226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6394.54 | −1.17726 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2783.39 | 0.507498 | 0.253749 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253749 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3002.13 | 0.542143 | 0.271071 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271071 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3773.81 | −0.668638 | −0.334319 | − | 0.942460i | \(-0.608506\pi\) | ||||
−0.334319 | + | 0.942460i | \(0.608506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16889.4 | 2.96435 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12623.0 | −2.19486 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6860.04 | −1.18174 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3768.61 | −0.643215 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7397.60 | 1.25104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 975.878 | 0.162052 | 0.0810259 | − | 0.996712i | \(-0.474180\pi\) | ||||
0.0810259 | + | 0.996712i | \(0.474180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −824.760 | −0.135725 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1087.75 | 0.177404 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3563.93 | −0.576083 | −0.288041 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288041 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9644.75 | −1.54522 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8235.04 | 1.30778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2406.17 | −0.375490 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1155.35 | 0.178740 | 0.0893698 | − | 0.995999i | \(-0.471515\pi\) | ||||
0.0893698 | + | 0.995999i | \(0.471515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4693.29 | 0.719845 | 0.359922 | − | 0.932982i | \(-0.382803\pi\) | ||||
0.359922 | + | 0.932982i | \(0.382803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3963.70 | 0.602754 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13257.1 | 1.99888 | 0.999439 | − | 0.0335035i | \(-0.0106665\pi\) | ||||
0.999439 | + | 0.0335035i | \(0.0106665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 554.598 | 0.0829155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1786.62 | 0.262658 | 0.131329 | − | 0.991339i | \(-0.458075\pi\) | ||||
0.131329 | + | 0.991339i | \(0.458075\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10105.6 | 1.47334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12777.1 | −1.84745 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1866.54 | 0.267668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6403.51 | 0.910791 | 0.455395 | − | 0.890289i | \(-0.349498\pi\) | ||||
0.455395 | + | 0.890289i | \(0.349498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2829.93 | 0.399242 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12170.2 | 1.68941 | 0.844705 | − | 0.535232i | \(-0.179776\pi\) | ||||
0.844705 | + | 0.535232i | \(0.179776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7016.78 | −0.966253 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11051.5 | −1.50977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2565.68 | 0.347732 | 0.173866 | − | 0.984769i | \(-0.444374\pi\) | ||||
0.173866 | + | 0.984769i | \(0.444374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6735.84 | −0.905742 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6609.16 | −0.881755 | −0.440878 | − | 0.897567i | \(-0.645333\pi\) | ||||
−0.440878 | + | 0.897567i | \(0.645333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1720.00 | 0.225924 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8887.49 | 1.15839 | 0.579195 | − | 0.815189i | \(-0.303367\pi\) | ||||
0.579195 | + | 0.815189i | \(0.303367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4033.35 | −0.521676 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5384.97 | −0.691185 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4313.25 | −0.549426 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8871.90 | −1.12158 | −0.560791 | − | 0.827958i | \(-0.689503\pi\) | ||||
−0.560791 | + | 0.827958i | \(0.689503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1282.24 | −0.159681 | −0.0798404 | − | 0.996808i | \(-0.525441\pi\) | ||||
−0.0798404 | + | 0.996808i | \(0.525441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5388.55 | −0.666062 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4643.81 | 0.569760 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4831.39 | 0.588411 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7686.63 | 0.929289 | 0.464645 | − | 0.885497i | \(-0.346182\pi\) | ||||
0.464645 | + | 0.885497i | \(0.346182\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13099.5 | −1.57214 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3777.46 | −0.446815 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4091.14 | 0.480442 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13364.1 | −1.55818 | −0.779092 | − | 0.626909i | \(-0.784320\pi\) | ||||
−0.779092 | + | 0.626909i | \(0.784320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1781.20 | 0.206201 | 0.103100 | − | 0.994671i | \(-0.467124\pi\) | ||||
0.103100 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1332.41 | 0.153154 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5178.27 | −0.591019 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13658.3 | 1.53713 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7582.35 | 0.847399 | 0.423700 | − | 0.905803i | \(-0.360731\pi\) | ||||
0.423700 | + | 0.905803i | \(0.360731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8642.25 | −0.959169 | −0.479585 | − | 0.877496i | \(-0.659213\pi\) | ||||
−0.479585 | + | 0.877496i | \(0.659213\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9059.12 | −0.998510 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9974.33 | 1.09185 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14212.6 | −1.54517 | −0.772586 | − | 0.634910i | \(-0.781037\pi\) | ||||
−0.772586 | + | 0.634910i | \(0.781037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7769.56 | 0.833280 | 0.416640 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416640 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1125.91 | −0.119940 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10969.2 | 1.16069 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7691.17 | −0.808393 | −0.404197 | − | 0.914672i | \(-0.632449\pi\) | ||||
−0.404197 | + | 0.914672i | \(0.632449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16577.6 | −1.73083 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6782.33 | 0.703447 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13384.2 | −1.36999 | −0.684996 | − | 0.728547i | \(-0.740196\pi\) | ||||
−0.684996 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5446.34 | 0.553841 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5451.80 | 0.550793 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13193.4 | 1.32430 | 0.662148 | − | 0.749373i | \(-0.269645\pi\) | ||||
0.662148 | + | 0.749373i | \(0.269645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4417.10 | −0.440512 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2338.19 | 0.231688 | 0.115844 | − | 0.993267i | \(-0.463043\pi\) | ||||
0.115844 | + | 0.993267i | \(0.463043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10208.8 | −0.998716 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10075.6 | −0.979448 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12805.7 | 1.23698 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 364.760 | 0.0350131 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18524.2 | 1.76700 | 0.883501 | − | 0.468430i | \(-0.155180\pi\) | ||||
0.883501 | + | 0.468430i | \(0.155180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3161.39 | −0.299682 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1303.21 | 0.122012 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5757.07 | −0.535684 | −0.267842 | − | 0.963463i | \(-0.586310\pi\) | ||||
−0.267842 | + | 0.963463i | \(0.586310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9638.71 | 0.891365 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10593.6 | 0.973692 | 0.486846 | − | 0.873488i | \(-0.338147\pi\) | ||||
0.486846 | + | 0.873488i | \(0.338147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15185.4 | −1.38725 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3025.93 | 0.274758 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3096.62 | 0.277803 | 0.138901 | − | 0.990306i | \(-0.455643\pi\) | ||||
0.138901 | + | 0.990306i | \(0.455643\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3769.30 | −0.336127 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3149.14 | −0.279151 | −0.139576 | − | 0.990211i | \(-0.544574\pi\) | ||||
−0.139576 | + | 0.990211i | \(0.544574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5970.17 | −0.526078 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4426.61 | 0.387757 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9133.85 | 0.795384 | 0.397692 | − | 0.917519i | \(-0.369811\pi\) | ||||
0.397692 | + | 0.917519i | \(0.369811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13468.6 | −1.15917 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5430.28 | −0.464635 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7805.20 | −0.663969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21780.9 | −1.84215 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5117.77 | 0.430353 | 0.215176 | − | 0.976575i | \(-0.430967\pi\) | ||||
0.215176 | + | 0.976575i | \(0.430967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5868.51 | 0.490654 | 0.245327 | − | 0.969440i | \(-0.421105\pi\) | ||||
0.245327 | + | 0.969440i | \(0.421105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7404.17 | −0.612012 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6302.61 | −0.518008 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2530.62 | −0.206817 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10847.4 | 0.881527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10719.6 | −0.866257 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3500.91 | −0.281332 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8280.32 | −0.658038 | −0.329019 | − | 0.944323i | \(-0.606718\pi\) | ||||
−0.329019 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9467.89 | 0.748262 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6282.10 | 0.493753 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16832.7 | −1.31575 | −0.657875 | − | 0.753127i | \(-0.728545\pi\) | ||||
−0.657875 | + | 0.753127i | \(0.728545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4991.24 | −0.388017 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37552.8 | 2.90346 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2591.45 | −0.198200 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10509.3 | 0.799450 | 0.399725 | − | 0.916635i | \(-0.369106\pi\) | ||||
0.399725 | + | 0.916635i | \(0.369106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6592.94 | 0.498840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18767.2 | 1.41239 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 333.004 | 0.0249280 | 0.0124640 | − | 0.999922i | \(-0.496032\pi\) | ||||
0.0124640 | + | 0.999922i | \(0.496032\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8190.39 | −0.609862 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15088.2 | 1.11166 | 0.555828 | − | 0.831298i | \(-0.312401\pi\) | ||||
0.555828 | + | 0.831298i | \(0.312401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1834.44 | 0.134446 | 0.0672232 | − | 0.997738i | \(-0.478586\pi\) | ||||
0.0672232 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4860.85 | 0.354389 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7529.08 | 0.546060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8516.30 | −0.614451 | −0.307225 | − | 0.951637i | \(-0.599401\pi\) | ||||
−0.307225 | + | 0.951637i | \(0.599401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3394.47 | 0.243643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2136.74 | −0.151792 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1980.00 | −0.139937 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23957.0 | 1.68452 | 0.842258 | − | 0.539074i | \(-0.181226\pi\) | ||||
0.842258 | + | 0.539074i | \(0.181226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18310.2 | 1.28092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10520.7 | 0.732254 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11730.9 | −0.812361 | −0.406181 | − | 0.913793i | \(-0.633140\pi\) | ||||
−0.406181 | + | 0.913793i | \(0.633140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26068.0 | −1.78709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4631.35 | −0.315913 | −0.157956 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157956 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25359.8 | 1.72121 | 0.860606 | − | 0.509272i | \(-0.170085\pi\) | ||||
0.860606 | + | 0.509272i | \(0.170085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2105.79 | −0.142213 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10850.4 | −0.729142 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 124.739 | 0.00834103 | 0.00417052 | − | 0.999991i | \(-0.498672\pi\) | ||||
0.00417052 | + | 0.999991i | \(0.498672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5107.28 | 0.338165 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17185.1 | −1.13230 | −0.566149 | − | 0.824303i | \(-0.691567\pi\) | ||||
−0.566149 | + | 0.824303i | \(0.691567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8891.83 | 0.583013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25988.1 | −1.69569 | −0.847844 | − | 0.530246i | \(-0.822100\pi\) | ||||
−0.847844 | + | 0.530246i | \(0.822100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18885.2 | −1.22627 | −0.613135 | − | 0.789978i | \(-0.710092\pi\) | ||||
−0.613135 | + | 0.789978i | \(0.710092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7918.84 | −0.511710 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6330.97 | 0.405182 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46410.6 | −2.95608 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4343.93 | −0.275364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6552.95 | 0.413421 | 0.206710 | − | 0.978402i | \(-0.433724\pi\) | ||||
0.206710 | + | 0.978402i | \(0.433724\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5169.76 | 0.324612 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5720.12 | −0.357474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1073.65 | −0.0664680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27671.0 | −1.70505 | −0.852525 | − | 0.522686i | \(-0.824930\pi\) | ||||
−0.852525 | + | 0.522686i | \(0.824930\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27154.8 | −1.66544 | −0.832722 | − | 0.553691i | \(-0.813219\pi\) | ||||
−0.832722 | + | 0.553691i | \(0.813219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5404.35 | 0.329917 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27322.6 | 1.66022 | 0.830110 | − | 0.557600i | \(-0.188278\pi\) | ||||
0.830110 | + | 0.557600i | \(0.188278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14824.2 | 0.896612 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1432.86 | 0.0858685 | 0.0429342 | − | 0.999078i | \(-0.486329\pi\) | ||||
0.0429342 | + | 0.999078i | \(0.486329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4572.95 | −0.272794 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3613.45 | −0.214572 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12914.0 | −0.763367 | −0.381684 | − | 0.924293i | \(-0.624656\pi\) | ||||
−0.381684 | + | 0.924293i | \(0.624656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10068.8 | 0.592485 | 0.296243 | − | 0.955113i | \(-0.404266\pi\) | ||||
0.296243 | + | 0.955113i | \(0.404266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12280.2 | −0.719343 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22079.2 | 1.28172 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26628.3 | −1.53888 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29238.4 | 1.68217 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1686.86 | −0.0966174 | −0.0483087 | − | 0.998832i | \(-0.515383\pi\) | ||||
−0.0483087 | + | 0.998832i | \(0.515383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10166.7 | −0.579728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22535.0 | 1.27931 | 0.639654 | − | 0.768663i | \(-0.279078\pi\) | ||||
0.639654 | + | 0.768663i | \(0.279078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31141.7 | 1.75235 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29406.1 | 1.64743 | 0.823714 | − | 0.567006i | \(-0.191898\pi\) | ||||
0.823714 | + | 0.567006i | \(0.191898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11124.2 | −0.620485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35774.6 | 1.98673 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1398.16 | 0.0773089 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 251.526 | 0.0138473 | 0.00692365 | − | 0.999976i | \(-0.497796\pi\) | ||||
0.00692365 | + | 0.999976i | \(0.497796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3474.23 | 0.189619 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14905.0 | 0.809993 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1290.02 | −0.0698039 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6188.42 | −0.333429 | −0.166714 | − | 0.986005i | \(-0.553316\pi\) | ||||
−0.166714 | + | 0.986005i | \(0.553316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10742.4 | 0.576324 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4186.53 | 0.223651 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27439.4 | 1.45347 | 0.726734 | − | 0.686919i | \(-0.241037\pi\) | ||||
0.726734 | + | 0.686919i | \(0.241037\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8350.07 | 0.440439 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10765.5 | 0.565456 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11598.7 | 0.606667 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31648.3 | 1.64844 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12278.5 | −0.636871 | −0.318436 | − | 0.947944i | \(-0.603157\pi\) | ||||
−0.318436 | + | 0.947944i | \(0.603157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17257.5 | 0.887711 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28346.6 | 1.45209 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8576.11 | 0.437510 | 0.218755 | − | 0.975780i | \(-0.429800\pi\) | ||||
0.218755 | + | 0.975780i | \(0.429800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7993.00 | 0.406086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9059.06 | 0.458360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12874.8 | 0.648762 | 0.324381 | − | 0.945926i | \(-0.394844\pi\) | ||||
0.324381 | + | 0.945926i | \(0.394844\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12335.6 | 0.616537 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19917.3 | −0.991432 | −0.495716 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495716 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30368.5 | 1.50555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22672.6 | −1.11948 | −0.559741 | − | 0.828667i | \(-0.689100\pi\) | ||||
−0.559741 | + | 0.828667i | \(0.689100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9315.16 | 0.458095 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7312.83 | 0.358183 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20953.6 | 1.01812 | 0.509059 | − | 0.860732i | \(-0.329994\pi\) | ||||
0.509059 | + | 0.860732i | \(0.329994\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28571.0 | 1.38272 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5759.60 | 0.277633 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12684.5 | −0.609018 | −0.304509 | − | 0.952510i | \(-0.598492\pi\) | ||||
−0.304509 | + | 0.952510i | \(0.598492\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27287.1 | −1.30495 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33663.7 | 1.60356 | 0.801779 | − | 0.597621i | \(-0.203887\pi\) | ||||
0.801779 | + | 0.597621i | \(0.203887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2720.63 | −0.128581 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9700.14 | −0.456652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20358.4 | 0.954672 | 0.477336 | − | 0.878721i | \(-0.341602\pi\) | ||||
0.477336 | + | 0.878721i | \(0.341602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42602.0 | 1.98998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 330.841 | 0.0153940 | 0.00769698 | − | 0.999970i | \(-0.497550\pi\) | ||||
0.00769698 | + | 0.999970i | \(0.497550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13821.4 | 0.640618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36859.4 | −1.69528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6289.39 | 0.288159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29814.0 | −1.36075 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8669.36 | −0.394169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6762.20 | 0.306285 | 0.153143 | − | 0.988204i | \(-0.451061\pi\) | ||||
0.153143 | + | 0.988204i | \(0.451061\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7471.50 | 0.337126 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19132.0 | −0.856741 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1146.10 | 0.0511296 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23848.2 | −1.05991 | −0.529954 | − | 0.848027i | \(-0.677791\pi\) | ||||
−0.529954 | + | 0.848027i | \(0.677791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7017.69 | 0.310723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2179.66 | 0.0961478 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21167.3 | 0.930235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 863.051 | 0.0376466 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −927.139 | −0.0402923 | −0.0201462 | − | 0.999797i | \(-0.506413\pi\) | ||||
−0.0201462 | + | 0.999797i | \(0.506413\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4288.65 | −0.185690 | −0.0928451 | − | 0.995681i | \(-0.529596\pi\) | ||||
−0.0928451 | + | 0.995681i | \(0.529596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2218.84 | 0.0957171 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8185.26 | 0.351800 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22402.7 | −0.959329 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27752.0 | 1.17972 | 0.589862 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589862 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8690.15 | −0.368068 | −0.184034 | − | 0.982920i | \(-0.558916\pi\) | ||||
−0.184034 | + | 0.982920i | \(0.558916\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35032.9 | −1.47841 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29503.0 | −1.24053 | −0.620267 | − | 0.784391i | \(-0.712976\pi\) | ||||
−0.620267 | + | 0.784391i | \(0.712976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20276.3 | 0.849488 | 0.424744 | − | 0.905314i | \(-0.360364\pi\) | ||||
0.424744 | + | 0.905314i | \(0.360364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12095.4 | −0.504917 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3200.92 | −0.132661 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14536.9 | −0.600320 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5229.63 | 0.215193 | 0.107596 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107596 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58737.9 | 2.40838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29829.5 | −1.21872 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3759.11 | 0.153038 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19830.2 | −0.801616 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6315.96 | 0.254416 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16423.9 | 0.659255 | 0.329628 | − | 0.944111i | \(-0.393077\pi\) | ||||
0.329628 | + | 0.944111i | \(0.393077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6728.01 | 0.269115 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30991.8 | −1.23531 | −0.617655 | − | 0.786449i | \(-0.711917\pi\) | ||||
−0.617655 | + | 0.786449i | \(0.711917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32514.3 | −1.29147 | −0.645735 | − | 0.763561i | \(-0.723449\pi\) | ||||
−0.645735 | + | 0.763561i | \(0.723449\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17365.6 | −0.684971 | −0.342486 | − | 0.939523i | \(-0.611269\pi\) | ||||
−0.342486 | + | 0.939523i | \(0.611269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18496.5 | −0.727053 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13010.9 | 0.509659 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48914.2 | −1.90944 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8071.73 | −0.314007 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2522.90 | −0.0978089 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20606.3 | −0.793417 | −0.396709 | − | 0.917945i | \(-0.629848\pi\) | ||||
−0.396709 | + | 0.917945i | \(0.629848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9815.58 | 0.376645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4704.88 | 0.179922 | 0.0899610 | − | 0.995945i | \(-0.471326\pi\) | ||||
0.0899610 | + | 0.995945i | \(0.471326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13075.1 | 0.498313 | 0.249157 | − | 0.968463i | \(-0.419847\pi\) | ||||
0.249157 | + | 0.968463i | \(0.419847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7951.38 | −0.302014 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44569.2 | 1.68714 | 0.843568 | − | 0.537023i | \(-0.180451\pi\) | ||||
0.843568 | + | 0.537023i | \(0.180451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52662.8 | 1.98010 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17354.5 | −0.650331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2973.00 | −0.111035 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17855.1 | 0.664622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40531.5 | 1.50367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1921.15 | 0.0710354 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8040.20 | 0.295321 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16003.3 | 0.585866 | 0.292933 | − | 0.956133i | \(-0.405369\pi\) | ||||
0.292933 | + | 0.956133i | \(0.405369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11557.7 | 0.421722 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10072.4 | −0.366315 | −0.183157 | − | 0.983084i | \(-0.558632\pi\) | ||||
−0.183157 | + | 0.983084i | \(0.558632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42838.1 | −1.55283 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15682.8 | −0.566621 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45278.2 | −1.62523 | −0.812617 | − | 0.582799i | \(-0.801958\pi\) | ||||
−0.812617 | + | 0.582799i | \(0.801958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17312.5 | 0.619398 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4115.42 | −0.146761 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8108.82 | 0.288234 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10512.6 | 0.372468 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8136.58 | 0.287355 | 0.143677 | − | 0.989625i | \(-0.454107\pi\) | ||||
0.143677 | + | 0.989625i | \(0.454107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16930.7 | −0.594091 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15937.3 | 0.557437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34741.9 | −1.21128 | −0.605640 | − | 0.795739i | \(-0.707083\pi\) | ||||
−0.605640 | + | 0.795739i | \(0.707083\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18261.3 | −0.634648 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37457.6 | −1.29764 | −0.648822 | − | 0.760940i | \(-0.724738\pi\) | ||||
−0.648822 | + | 0.760940i | \(0.724738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21671.4 | −0.748376 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7552.29 | 0.259152 | 0.129576 | − | 0.991570i | \(-0.458638\pi\) | ||||
0.129576 | + | 0.991570i | \(0.458638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13850.7 | −0.473776 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22955.2 | 0.782727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25745.6 | −0.875111 | −0.437556 | − | 0.899191i | \(-0.644156\pi\) | ||||
−0.437556 | + | 0.899191i | \(0.644156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4127.86 | 0.139869 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −102734. | −3.47015 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10028.4 | −0.336627 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20752.1 | 0.694422 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2882.61 | 0.0961601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31718.6 | −1.05481 | −0.527406 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527406 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41728.0 | 1.38338 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39308.8 | 1.29916 | 0.649578 | − | 0.760295i | \(-0.274946\pi\) | ||||
0.649578 | + | 0.760295i | \(0.274946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22923.5 | 0.752965 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5238.61 | −0.171543 | −0.0857717 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857717 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12768.3 | −0.416830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12161.6 | −0.395810 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25163.5 | −0.816472 | −0.408236 | − | 0.912876i | \(-0.633856\pi\) | ||||
−0.408236 | + | 0.912876i | \(0.633856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8934.22 | 0.289003 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13171.6 | −0.423492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43561.1 | −1.39633 | −0.698166 | − | 0.715936i | \(-0.746000\pi\) | ||||
−0.698166 | + | 0.715936i | \(0.746000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5936.04 | −0.189702 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22137.1 | −0.705320 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50840.3 | 1.61497 | 0.807487 | − | 0.589885i | \(-0.200827\pi\) | ||||
0.807487 | + | 0.589885i | \(0.200827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8528.60 | −0.270103 |
(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 | 784.4.a.ba.1.1 | 2 | ||
4.3 | odd | 2 | 196.4.a.g.1.2 | 2 | |||
7.3 | odd | 6 | 112.4.i.d.65.1 | 4 | |||
7.5 | odd | 6 | 112.4.i.d.81.1 | 4 | |||
7.6 | odd | 2 | 784.4.a.u.1.2 | 2 | |||
12.11 | even | 2 | 1764.4.a.n.1.2 | 2 | |||
28.3 | even | 6 | 28.4.e.a.9.2 | ✓ | 4 | ||
28.11 | odd | 6 | 196.4.e.g.177.1 | 4 | |||
28.19 | even | 6 | 28.4.e.a.25.2 | yes | 4 | ||
28.23 | odd | 6 | 196.4.e.g.165.1 | 4 | |||
28.27 | even | 2 | 196.4.a.e.1.1 | 2 | |||
56.3 | even | 6 | 448.4.i.h.65.1 | 4 | |||
56.5 | odd | 6 | 448.4.i.g.193.2 | 4 | |||
56.19 | even | 6 | 448.4.i.h.193.1 | 4 | |||
56.45 | odd | 6 | 448.4.i.g.65.2 | 4 | |||
84.11 | even | 6 | 1764.4.k.ba.1549.1 | 4 | |||
84.23 | even | 6 | 1764.4.k.ba.361.1 | 4 | |||
84.47 | odd | 6 | 252.4.k.c.109.2 | 4 | |||
84.59 | odd | 6 | 252.4.k.c.37.2 | 4 | |||
84.83 | odd | 2 | 1764.4.a.z.1.1 | 2 | |||
140.3 | odd | 12 | 700.4.r.d.149.2 | 8 | |||
140.19 | even | 6 | 700.4.i.g.501.1 | 4 | |||
140.47 | odd | 12 | 700.4.r.d.249.2 | 8 | |||
140.59 | even | 6 | 700.4.i.g.401.1 | 4 | |||
140.87 | odd | 12 | 700.4.r.d.149.3 | 8 | |||
140.103 | odd | 12 | 700.4.r.d.249.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.e.a.9.2 | ✓ | 4 | 28.3 | even | 6 | ||
28.4.e.a.25.2 | yes | 4 | 28.19 | even | 6 | ||
112.4.i.d.65.1 | 4 | 7.3 | odd | 6 | |||
112.4.i.d.81.1 | 4 | 7.5 | odd | 6 | |||
196.4.a.e.1.1 | 2 | 28.27 | even | 2 | |||
196.4.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
196.4.e.g.165.1 | 4 | 28.23 | odd | 6 | |||
196.4.e.g.177.1 | 4 | 28.11 | odd | 6 | |||
252.4.k.c.37.2 | 4 | 84.59 | odd | 6 | |||
252.4.k.c.109.2 | 4 | 84.47 | odd | 6 | |||
448.4.i.g.65.2 | 4 | 56.45 | odd | 6 | |||
448.4.i.g.193.2 | 4 | 56.5 | odd | 6 | |||
448.4.i.h.65.1 | 4 | 56.3 | even | 6 | |||
448.4.i.h.193.1 | 4 | 56.19 | even | 6 | |||
700.4.i.g.401.1 | 4 | 140.59 | even | 6 | |||
700.4.i.g.501.1 | 4 | 140.19 | even | 6 | |||
700.4.r.d.149.2 | 8 | 140.3 | odd | 12 | |||
700.4.r.d.149.3 | 8 | 140.87 | odd | 12 | |||
700.4.r.d.249.2 | 8 | 140.47 | odd | 12 | |||
700.4.r.d.249.3 | 8 | 140.103 | odd | 12 | |||
784.4.a.u.1.2 | 2 | 7.6 | odd | 2 | |||
784.4.a.ba.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1764.4.a.n.1.2 | 2 | 12.11 | even | 2 | |||
1764.4.a.z.1.1 | 2 | 84.83 | odd | 2 | |||
1764.4.k.ba.361.1 | 4 | 84.23 | even | 6 | |||
1764.4.k.ba.1549.1 | 4 | 84.11 | even | 6 |