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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 35x^{2} + 36x + 194 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.11692\) 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 | ||||||||
\(3\) | −3.57956 | −0.688886 | −0.344443 | − | 0.938807i | \(-0.611932\pi\) | ||||
−0.344443 | + | 0.938807i | \(0.611932\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.4791 | −1.20560 | −0.602802 | − | 0.797891i | \(-0.705949\pi\) | ||||
−0.602802 | + | 0.797891i | \(0.705949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.1868 | −0.525436 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.813227 | −0.0222906 | −0.0111453 | − | 0.999938i | \(-0.503548\pi\) | ||||
−0.0111453 | + | 0.999938i | \(0.503548\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.9564 | 0.745781 | 0.372891 | − | 0.927875i | \(-0.378367\pi\) | ||||
0.372891 | + | 0.927875i | \(0.378367\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 48.2490 | 0.830523 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 117.732 | 1.67966 | 0.839829 | − | 0.542851i | \(-0.182655\pi\) | ||||
0.839829 | + | 0.542851i | \(0.182655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 93.2913 | 1.12645 | 0.563224 | − | 0.826304i | \(-0.309561\pi\) | ||||
0.563224 | + | 0.826304i | \(0.309561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −120.249 | −1.09016 | −0.545079 | − | 0.838384i | \(-0.683501\pi\) | ||||
−0.545079 | + | 0.838384i | \(0.683501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56.6848 | 0.453479 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 147.430 | 1.05085 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.56420 | 0.0548390 | 0.0274195 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274195 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82.1070 | 0.475705 | 0.237852 | − | 0.971301i | \(-0.423557\pi\) | ||||
0.237852 | + | 0.971301i | \(0.423557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91099 | 0.0153557 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.8132 | 0.128023 | 0.0640117 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640117 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −125.128 | −0.513758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.5291 | −0.268654 | −0.134327 | − | 0.990937i | \(-0.542887\pi\) | ||||
−0.134327 | + | 0.990937i | \(0.542887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −417.179 | −1.47952 | −0.739758 | − | 0.672873i | \(-0.765060\pi\) | ||||
−0.739758 | + | 0.672873i | \(0.765060\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 191.224 | 0.633467 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −338.261 | −1.04980 | −0.524899 | − | 0.851165i | \(-0.675897\pi\) | ||||
−0.524899 | + | 0.851165i | \(0.675897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −421.428 | −1.15709 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 149.121 | 0.386477 | 0.193239 | − | 0.981152i | \(-0.438101\pi\) | ||||
0.193239 | + | 0.981152i | \(0.438101\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9615 | 0.0268737 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −333.942 | −0.775994 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 94.1828 | 0.207823 | 0.103911 | − | 0.994587i | \(-0.466864\pi\) | ||||
0.103911 | + | 0.994587i | \(0.466864\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −120.525 | −0.252977 | −0.126488 | − | 0.991968i | \(-0.540371\pi\) | ||||
−0.126488 | + | 0.991968i | \(0.540371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −471.179 | −0.899116 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 792.366 | 1.44482 | 0.722410 | − | 0.691465i | \(-0.243035\pi\) | ||||
0.722410 | + | 0.691465i | \(0.243035\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 430.438 | 0.750995 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −449.128 | −0.750729 | −0.375364 | − | 0.926877i | \(-0.622482\pi\) | ||||
−0.375364 | + | 0.926877i | \(0.622482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −469.420 | −0.752623 | −0.376311 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376311 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −202.907 | −0.312395 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1019.85 | 1.45243 | 0.726217 | − | 0.687465i | \(-0.241277\pi\) | ||||
0.726217 | + | 0.687465i | \(0.241277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −144.693 | −0.198481 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 104.253 | 0.137870 | 0.0689352 | − | 0.997621i | \(-0.478040\pi\) | ||||
0.0689352 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1586.91 | −2.02500 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −30.6560 | −0.0377778 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1572.92 | −1.87336 | −0.936680 | − | 0.350185i | \(-0.886119\pi\) | ||||
−0.936680 | + | 0.350185i | \(0.886119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −293.906 | −0.327706 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1257.48 | −1.35805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 550.057 | 0.575772 | 0.287886 | − | 0.957665i | \(-0.407048\pi\) | ||||
0.287886 | + | 0.957665i | \(0.407048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.5371 | 0.0117123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −65.7169 | −0.0647433 | −0.0323717 | − | 0.999476i | \(-0.510306\pi\) | ||||
−0.0323717 | + | 0.999476i | \(0.510306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1829.35 | −1.75001 | −0.875005 | − | 0.484113i | \(-0.839142\pi\) | ||||
−0.875005 | + | 0.484113i | \(0.839142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −861.377 | −0.778248 | −0.389124 | − | 0.921185i | \(-0.627222\pi\) | ||||
−0.389124 | + | 0.921185i | \(0.627222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1620.52 | −1.42401 | −0.712007 | − | 0.702173i | \(-0.752213\pi\) | ||||
−0.712007 | + | 0.702173i | \(0.752213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −103.139 | −0.0881935 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 380.409 | 0.316689 | 0.158344 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158344 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1620.84 | 1.31430 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −495.918 | −0.391860 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.34 | −0.999503 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252.463 | 0.185072 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 920.824 | 0.658888 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −958.358 | −0.669610 | −0.334805 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334805 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1493.32 | 1.01922 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1152.16 | −0.768431 | −0.384216 | − | 0.923243i | \(-0.625528\pi\) | ||||
−0.384216 | + | 0.923243i | \(0.625528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1987.22 | −1.26691 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 357.377 | 0.222867 | 0.111434 | − | 0.993772i | \(-0.464456\pi\) | ||||
0.111434 | + | 0.993772i | \(0.464456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2736.29 | 1.66970 | 0.834852 | − | 0.550475i | \(-0.185553\pi\) | ||||
0.834852 | + | 0.550475i | \(0.185553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1210.83 | 0.723191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.4275 | −0.0166239 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −115.437 | −0.0661141 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1409.94 | 0.775212 | 0.387606 | − | 0.921825i | \(-0.373302\pi\) | ||||
0.387606 | + | 0.921825i | \(0.373302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2352.35 | −1.26776 | −0.633879 | − | 0.773432i | \(-0.718538\pi\) | ||||
−0.633879 | + | 0.773432i | \(0.718538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1670.24 | −0.882553 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1106.72 | −0.573511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1213.82 | 0.617029 | 0.308514 | − | 0.951220i | \(-0.400168\pi\) | ||||
0.308514 | + | 0.951220i | \(0.400168\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −533.786 | −0.266239 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 722.774 | 0.347313 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −39.2374 | −0.0185129 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −753.016 | −0.348923 | −0.174462 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174462 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −975.051 | −0.443810 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1323.50 | −0.591876 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1859.14 | −0.817038 | −0.408519 | − | 0.912750i | \(-0.633955\pi\) | ||||
−0.408519 | + | 0.912750i | \(0.633955\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −337.133 | −0.143166 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 522.825 | 0.218312 | 0.109156 | − | 0.994025i | \(-0.465185\pi\) | ||||
0.109156 | + | 0.994025i | \(0.465185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2901.38 | 1.19148 | 0.595740 | − | 0.803177i | \(-0.296859\pi\) | ||||
0.595740 | + | 0.803177i | \(0.296859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 431.424 | 0.174272 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −388.375 | −0.154345 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −95.7427 | −0.0374407 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2604.35 | −0.986619 | −0.493309 | − | 0.869854i | \(-0.664213\pi\) | ||||
−0.493309 | + | 0.869854i | \(0.664213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 676.245 | 0.252214 | 0.126107 | − | 0.992017i | \(-0.459752\pi\) | ||||
0.126107 | + | 0.992017i | \(0.459752\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1686.61 | 0.619389 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3685.99 | −1.33308 | −0.666538 | − | 0.745471i | \(-0.732225\pi\) | ||||
−0.666538 | + | 0.745471i | \(0.732225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 799.801 | 0.284907 | 0.142453 | − | 0.989802i | \(-0.454501\pi\) | ||||
0.142453 | + | 0.989802i | \(0.454501\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2836.32 | −0.995316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 950.665 | 0.323890 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1705.95 | 0.572809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −75.8670 | −0.0251092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 667.385 | 0.217747 | 0.108874 | − | 0.994056i | \(-0.465276\pi\) | ||||
0.108874 | + | 0.994056i | \(0.465276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1607.68 | 0.517166 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5623.18 | 1.78371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1680.32 | 0.518471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4115.48 | 1.25266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2646.82 | −0.794818 | −0.397409 | − | 0.917642i | \(-0.630091\pi\) | ||||
−0.397409 | + | 0.917642i | \(0.630091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −804.175 | −0.238274 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4121.11 | −1.20497 | −0.602485 | − | 0.798131i | \(-0.705822\pi\) | ||||
−0.602485 | + | 0.798131i | \(0.705822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4066.92 | 1.17358 | 0.586790 | − | 0.809739i | \(-0.300391\pi\) | ||||
0.586790 | + | 0.809739i | \(0.300391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3904.67 | −1.09787 | −0.548934 | − | 0.835865i | \(-0.684966\pi\) | ||||
−0.548934 | + | 0.835865i | \(0.684966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4559.44 | 1.26564 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3650.62 | −1.00056 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5425.12 | −1.46829 | −0.734146 | − | 0.678991i | \(-0.762417\pi\) | ||||
−0.734146 | + | 0.678991i | \(0.762417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1602.89 | −0.428429 | −0.214215 | − | 0.976787i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976787i | \(0.568719\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3462.69 | −0.914121 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3261.13 | 0.840084 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −373.179 | −0.0949769 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3805.93 | −0.957085 | −0.478542 | − | 0.878064i | \(-0.658835\pi\) | ||||
−0.478542 | + | 0.878064i | \(0.658835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 97.7897 | 0.0243003 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5680.45 | 1.39499 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4589.34 | 1.11391 | 0.556956 | − | 0.830542i | \(-0.311969\pi\) | ||||
0.556956 | + | 0.830542i | \(0.311969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −121.498 | −0.0288144 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −877.175 | −0.205661 | −0.102831 | − | 0.994699i | \(-0.532790\pi\) | ||||
−0.102831 | + | 0.994699i | \(0.532790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2010.00 | −0.465938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5630.35 | 1.29053 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6123.55 | −1.38795 | −0.693977 | − | 0.719997i | \(-0.744143\pi\) | ||||
−0.693977 | + | 0.719997i | \(0.744143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3489.76 | 0.782243 | 0.391122 | − | 0.920339i | \(-0.372087\pi\) | ||||
0.391122 | + | 0.920339i | \(0.372087\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −46.0976 | −0.0101083 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4891.70 | −1.06106 | −0.530530 | − | 0.847666i | \(-0.678007\pi\) | ||||
−0.530530 | + | 0.847666i | \(0.678007\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1164.83 | −0.249952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6914.46 | 1.46791 | 0.733954 | − | 0.679199i | \(-0.237673\pi\) | ||||
0.733954 | + | 0.679199i | \(0.237673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3559.85 | −0.747742 | −0.373871 | − | 0.927481i | \(-0.621970\pi\) | ||||
−0.373871 | + | 0.927481i | \(0.621970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4501.22 | 0.935541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8947.80 | 1.82125 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1968.96 | −0.396641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3285.11 | 0.655011 | 0.327505 | − | 0.944849i | \(-0.393792\pi\) | ||||
0.327505 | + | 0.944849i | \(0.393792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1269.49 | −0.250552 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −119.894 | −0.0234242 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4203.47 | −0.813020 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 235.237 | 0.0446008 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1624.56 | 0.304990 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9094.65 | 1.69075 | 0.845373 | − | 0.534176i | \(-0.179378\pi\) | ||||
0.845373 | + | 0.534176i | \(0.179378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6548.26 | 1.20556 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8163.06 | 1.48838 | 0.744188 | − | 0.667971i | \(-0.232837\pi\) | ||||
0.744188 | + | 0.667971i | \(0.232837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2979.62 | 0.538076 | 0.269038 | − | 0.963130i | \(-0.413294\pi\) | ||||
0.269038 | + | 0.963130i | \(0.413294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3888.11 | −0.688889 | −0.344445 | − | 0.938807i | \(-0.611933\pi\) | ||||
−0.344445 | + | 0.938807i | \(0.611933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.96463 | −0.00122240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3083.35 | 0.536124 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10983.4 | 1.89205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1981.50 | 0.338196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5800.74 | 0.980983 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4893.03 | 0.812524 | 0.406262 | − | 0.913757i | \(-0.366832\pi\) | ||||
0.406262 | + | 0.913757i | \(0.366832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −408.767 | −0.0672681 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10680.3 | −1.74188 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1722.10 | −0.278364 | −0.139182 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139182 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1361.69 | −0.218163 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −66.7716 | −0.0106038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5801.90 | −0.905402 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 238.058 | 0.0368289 | 0.0184145 | − | 0.999830i | \(-0.494138\pi\) | ||||
0.0184145 | + | 0.999830i | \(0.494138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10053.1 | −1.54192 | −0.770959 | − | 0.636884i | \(-0.780223\pi\) | ||||
−0.770959 | + | 0.636884i | \(0.780223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5153.63 | 0.783706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3470.16 | −0.523224 | −0.261612 | − | 0.965173i | \(-0.584254\pi\) | ||||
−0.261612 | + | 0.965173i | \(0.584254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6053.82 | 0.905081 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1407.54 | −0.206928 | −0.103464 | − | 0.994633i | \(-0.532993\pi\) | ||||
−0.103464 | + | 0.994633i | \(0.532993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1844.27 | 0.268884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4762.02 | 0.688544 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6327.34 | 0.907364 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11133.0 | −1.58348 | −0.791742 | − | 0.610855i | \(-0.790826\pi\) | ||||
−0.791742 | + | 0.610855i | \(0.790826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1000.58 | 0.141160 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9025.94 | 1.25294 | 0.626468 | − | 0.779447i | \(-0.284500\pi\) | ||||
0.626468 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3296.14 | −0.453899 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 299.373 | 0.0408979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5855.75 | 0.793640 | 0.396820 | − | 0.917896i | \(-0.370114\pi\) | ||||
0.396820 | + | 0.917896i | \(0.370114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3430.50 | 0.461285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7788.03 | 1.03903 | 0.519517 | − | 0.854460i | \(-0.326112\pi\) | ||||
0.519517 | + | 0.854460i | \(0.326112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5918.42 | 0.777391 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3814.05 | −0.497121 | −0.248560 | − | 0.968616i | \(-0.579957\pi\) | ||||
−0.248560 | + | 0.968616i | \(0.579957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14157.1 | −1.83109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4124.21 | 0.529362 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13746.6 | −1.75106 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10165.3 | −1.28509 | −0.642545 | − | 0.766248i | \(-0.722121\pi\) | ||||
−0.642545 | + | 0.766248i | \(0.722121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11502.5 | 1.43244 | 0.716222 | − | 0.697873i | \(-0.245870\pi\) | ||||
0.716222 | + | 0.697873i | \(0.245870\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2870.16 | 0.354772 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1950.32 | 0.239289 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4317 | −0.00285372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3266.27 | 0.394882 | 0.197441 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197441 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1279.25 | −0.153530 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1405.23 | −0.166217 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9794.69 | −1.15024 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6822.93 | 0.795518 | 0.397759 | − | 0.917490i | \(-0.369788\pi\) | ||||
0.397759 | + | 0.917490i | \(0.369788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1431.63 | 0.165733 | 0.0828665 | − | 0.996561i | \(-0.473592\pi\) | ||||
0.0828665 | + | 0.996561i | \(0.473592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4798.83 | 0.551601 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6673.61 | 0.761689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 101.758 | 0.0114520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15142.2 | −1.69228 | −0.846141 | − | 0.532959i | \(-0.821080\pi\) | ||||
−0.846141 | + | 0.532959i | \(0.821080\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5475.65 | −0.607721 | −0.303860 | − | 0.952717i | \(-0.598276\pi\) | ||||
−0.303860 | + | 0.952717i | \(0.598276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 413.214 | 0.0455451 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11218.2 | −1.22801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1780.54 | −0.193578 | −0.0967890 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967890 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3259.64 | 0.349594 | 0.174797 | − | 0.984605i | \(-0.444073\pi\) | ||||
0.174797 | + | 0.984605i | \(0.444073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21201.5 | 2.25853 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5046.95 | −0.534033 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6826.19 | −0.717478 | −0.358739 | − | 0.933438i | \(-0.616793\pi\) | ||||
−0.358739 | + | 0.933438i | \(0.616793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 57.3562 | 0.00598846 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8420.37 | 0.873341 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3700.03 | 0.378731 | 0.189365 | − | 0.981907i | \(-0.439357\pi\) | ||||
0.189365 | + | 0.981907i | \(0.439357\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17357.3 | 1.76507 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9400.80 | −0.949759 | −0.474880 | − | 0.880051i | \(-0.657508\pi\) | ||||
−0.474880 | + | 0.880051i | \(0.657508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15483.9 | −1.55420 | −0.777102 | − | 0.629374i | \(-0.783311\pi\) | ||||
−0.777102 | + | 0.629374i | \(0.783311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3961.58 | 0.395084 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2205.62 | 0.218552 | 0.109276 | − | 0.994011i | \(-0.465147\pi\) | ||||
0.109276 | + | 0.994011i | \(0.465147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4344.94 | −0.425062 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 339.261 | 0.0329794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5288.20 | 0.510820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2115.54 | −0.203069 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2349.32 | −0.224098 | −0.112049 | − | 0.993703i | \(-0.535741\pi\) | ||||
−0.112049 | + | 0.993703i | \(0.535741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1007.21 | 0.0954775 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7414.25 | −0.694152 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10394.3 | −0.967167 | −0.483583 | − | 0.875298i | \(-0.660665\pi\) | ||||
−0.483583 | + | 0.875298i | \(0.660665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2587.21 | −0.239259 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12586.7 | −1.15689 | −0.578444 | − | 0.815722i | \(-0.696340\pi\) | ||||
−0.578444 | + | 0.815722i | \(0.696340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1008.28 | 0.0921108 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −155.509 | −0.0141204 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10627.9 | −0.953450 | −0.476725 | − | 0.879053i | \(-0.658176\pi\) | ||||
−0.476725 | + | 0.879053i | \(0.658176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2695.46 | 0.240368 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6719.02 | 0.595599 | 0.297800 | − | 0.954628i | \(-0.403747\pi\) | ||||
0.297800 | + | 0.954628i | \(0.403747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 885.802 | 0.0780548 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3490.25 | 0.305735 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3904.33 | 0.339993 | 0.169997 | − | 0.985445i | \(-0.445624\pi\) | ||||
0.169997 | + | 0.985445i | \(0.445624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13754.0 | 1.18373 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24657.9 | 2.10982 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 275.083 | 0.0234007 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6654.89 | 0.562846 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15699.7 | −1.32018 | −0.660092 | − | 0.751184i | \(-0.729483\pi\) | ||||
−0.660092 | + | 0.751184i | \(0.729483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10152.1 | −0.848794 | −0.424397 | − | 0.905476i | \(-0.639514\pi\) | ||||
−0.424397 | + | 0.905476i | \(0.639514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9666.61 | 0.799021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2292.83 | 0.188447 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1336.15 | −0.109198 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2465.44 | −0.200357 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11610.6 | 0.938258 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1871.48 | −0.150392 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19846.6 | −1.57722 | −0.788608 | − | 0.614896i | \(-0.789198\pi\) | ||||
−0.788608 | + | 0.614896i | \(0.789198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10385.7 | −0.820794 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21843.0 | 1.71679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22798.9 | 1.78210 | 0.891052 | − | 0.453901i | \(-0.149968\pi\) | ||||
0.891052 | + | 0.453901i | \(0.149968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1709.85 | 0.132923 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 798.965 | 0.0617733 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1390.21 | 0.106326 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17998.3 | −1.36914 | −0.684570 | − | 0.728947i | \(-0.740010\pi\) | ||||
−0.684570 | + | 0.728947i | \(0.740010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14583.1 | −1.10340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 342.717 | 0.0257923 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −195.636 | −0.0146449 | −0.00732246 | − | 0.999973i | \(-0.502331\pi\) | ||||
−0.00732246 | + | 0.999973i | \(0.502331\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5127.55 | −0.381801 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19660.4 | −1.44852 | −0.724260 | − | 0.689527i | \(-0.757818\pi\) | ||||
−0.724260 | + | 0.689527i | \(0.757818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15764.5 | 1.15538 | 0.577691 | − | 0.816255i | \(-0.303954\pi\) | ||||
0.577691 | + | 0.816255i | \(0.303954\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9322.42 | 0.679668 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6816.30 | −0.494364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22306.4 | 1.60941 | 0.804704 | − | 0.593676i | \(-0.202324\pi\) | ||||
0.804704 | + | 0.593676i | \(0.202324\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2420.66 | −0.173746 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −121.269 | −0.00861483 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6684.51 | 0.472428 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15953.2 | 1.12173 | 0.560866 | − | 0.827906i | \(-0.310468\pi\) | ||||
0.560866 | + | 0.827906i | \(0.310468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7659.87 | 0.535856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13194.2 | 0.918338 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3155.68 | −0.218530 | −0.109265 | − | 0.994013i | \(-0.534850\pi\) | ||||
−0.109265 | + | 0.994013i | \(0.534850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2862.93 | −0.196268 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25456.3 | −1.73642 | −0.868212 | − | 0.496194i | \(-0.834730\pi\) | ||||
−0.868212 | + | 0.496194i | \(0.834730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5580.96 | 0.378789 | 0.189395 | − | 0.981901i | \(-0.439347\pi\) | ||||
0.189395 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11241.1 | −0.759160 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17931.7 | 1.20500 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −381.133 | −0.0254855 | −0.0127427 | − | 0.999919i | \(-0.504056\pi\) | ||||
−0.0127427 | + | 0.999919i | \(0.504056\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11824.4 | −0.782919 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8235.98 | −0.542656 | −0.271328 | − | 0.962487i | \(-0.587463\pi\) | ||||
−0.271328 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3402.96 | −0.223123 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27419.8 | −1.78911 | −0.894555 | − | 0.446958i | \(-0.852507\pi\) | ||||
−0.894555 | + | 0.446958i | \(0.852507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16373.4 | 1.06317 | 0.531585 | − | 0.847005i | \(-0.321597\pi\) | ||||
0.531585 | + | 0.847005i | \(0.321597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17728.4 | −1.14560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19497.4 | −1.24784 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 271.570 | 0.0172974 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3392.24 | 0.215035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4059.60 | −0.256118 | −0.128059 | − | 0.991767i | \(-0.540875\pi\) | ||||
−0.128059 | + | 0.991767i | \(0.540875\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2388.94 | −0.150003 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12917.8 | 0.807284 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6371.68 | 0.394460 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6388.63 | −0.393660 | −0.196830 | − | 0.980438i | \(-0.563065\pi\) | ||||
−0.196830 | + | 0.980438i | \(0.563065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18308.0 | 1.12286 | 0.561428 | − | 0.827525i | \(-0.310252\pi\) | ||||
0.561428 | + | 0.827525i | \(0.310252\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20128.5 | −1.22877 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3303.90 | −0.200757 | −0.100379 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100379 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −76.5919 | −0.00463251 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4371.27 | 0.261961 | 0.130981 | − | 0.991385i | \(-0.458187\pi\) | ||||
0.130981 | + | 0.991385i | \(0.458187\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15530.0 | 0.926423 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6659.55 | 0.395455 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6259.75 | −0.370023 | −0.185012 | − | 0.982736i | \(-0.559232\pi\) | ||||
−0.185012 | + | 0.982736i | \(0.559232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14845.7 | −0.873574 | −0.436787 | − | 0.899565i | \(-0.643884\pi\) | ||||
−0.436787 | + | 0.899565i | \(0.643884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14731.6 | −0.862938 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1029.84 | −0.0597832 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9474.46 | 0.547539 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 98.0138 | 0.00563902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9409.13 | 0.538923 | 0.269462 | − | 0.963011i | \(-0.413154\pi\) | ||||
0.269462 | + | 0.963011i | \(0.413154\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8357.07 | 0.476539 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2950.63 | 0.167507 | 0.0837533 | − | 0.996487i | \(-0.473309\pi\) | ||||
0.0837533 | + | 0.996487i | \(0.473309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14751.8 | 0.830086 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6280.85 | −0.351874 | −0.175937 | − | 0.984401i | \(-0.556296\pi\) | ||||
−0.175937 | + | 0.984401i | \(0.556296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4817.11 | −0.268689 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14557.8 | −0.808463 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5212.72 | 0.288228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32763.2 | −1.80372 | −0.901861 | − | 0.432027i | \(-0.857798\pi\) | ||||
−0.901861 | + | 0.432027i | \(0.857798\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36882.5 | −2.01300 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8303.53 | −0.451246 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13977.0 | 0.756306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1775.97 | −0.0956883 | −0.0478442 | − | 0.998855i | \(-0.515235\pi\) | ||||
−0.0478442 | + | 0.998855i | \(0.515235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2688.02 | 0.144212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16320.8 | −0.871881 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8862.43 | 0.469444 | 0.234722 | − | 0.972063i | \(-0.424582\pi\) | ||||
0.234722 | + | 0.972063i | \(0.424582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14468.4 | −0.763162 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9873.28 | −0.518594 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 383.175 | 0.0200419 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19419.5 | 1.01149 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27499.2 | −1.42635 | −0.713177 | − | 0.700984i | \(-0.752744\pi\) | ||||
−0.713177 | + | 0.700984i | \(0.752744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5737.65 | 0.295139 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 485.460 | 0.0248683 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25434.9 | −1.29756 | −0.648781 | − | 0.760975i | \(-0.724721\pi\) | ||||
−0.648781 | + | 0.760975i | \(0.724721\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16301.6 | 0.828206 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49115.3 | −2.48508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24155.6 | −1.21720 | −0.608600 | − | 0.793477i | \(-0.708269\pi\) | ||||
−0.608600 | + | 0.793477i | \(0.708269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −644.373 | −0.0322060 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27512.9 | −1.36952 | −0.684762 | − | 0.728767i | \(-0.740094\pi\) | ||||
−0.684762 | + | 0.728767i | \(0.740094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11673.4 | −0.578722 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5995.09 | −0.296014 | −0.148007 | − | 0.988986i | \(-0.547286\pi\) | ||||
−0.148007 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19004.6 | −0.934598 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1479.01 | −0.0724420 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1545.09 | −0.0750747 | −0.0375373 | − | 0.999295i | \(-0.511951\pi\) | ||||
−0.0375373 | + | 0.999295i | \(0.511951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13623.6 | 0.659322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31707.5 | 1.52841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5157.82 | −0.247641 | −0.123820 | − | 0.992305i | \(-0.539515\pi\) | ||||
−0.123820 | + | 0.992305i | \(0.539515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −350.044 | −0.0167402 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3289.96 | −0.156716 | −0.0783581 | − | 0.996925i | \(-0.524968\pi\) | ||||
−0.0783581 | + | 0.996925i | \(0.524968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22513.2 | 1.06401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3292.29 | 0.154990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11146.5 | −0.522697 | −0.261348 | − | 0.965245i | \(-0.584167\pi\) | ||||
−0.261348 | + | 0.965245i | \(0.584167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16427.8 | −0.767358 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15830.2 | −0.736576 | −0.368288 | − | 0.929712i | \(-0.620056\pi\) | ||||
−0.368288 | + | 0.929712i | \(0.620056\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4654.22 | 0.215722 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6579.75 | −0.302624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 365.243 | 0.0167342 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1262.62 | 0.0576277 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16361.2 | −0.743892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15163.4 | 0.686809 | 0.343404 | − | 0.939188i | \(-0.388420\pi\) | ||||
0.343404 | + | 0.939188i | \(0.388420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3139.90 | 0.141677 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4213.10 | −0.188665 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7194.93 | 0.320978 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29398.3 | 1.30658 | 0.653289 | − | 0.757109i | \(-0.273389\pi\) | ||||
0.653289 | + | 0.757109i | \(0.273389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39824.1 | −1.76330 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22314.6 | 0.984331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 381.745 | 0.0167764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21919.6 | 0.956142 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20712.9 | −0.900155 | −0.450078 | − | 0.892989i | \(-0.648604\pi\) | ||||
−0.450078 | + | 0.892989i | \(0.648604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27369.9 | −1.18506 | −0.592532 | − | 0.805547i | \(-0.701872\pi\) | ||||
−0.592532 | + | 0.805547i | \(0.701872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12491.8 | −0.538876 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9742.31 | −0.418722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38919.2 | −1.66660 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35362.7 | −1.50325 | −0.751623 | − | 0.659592i | \(-0.770729\pi\) | ||||
−0.751623 | + | 0.659592i | \(0.770729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29190.4 | 1.23635 | 0.618174 | − | 0.786042i | \(-0.287873\pi\) | ||||
0.618174 | + | 0.786042i | \(0.287873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 165.009 | 0.00696349 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7302.08 | 0.307035 | 0.153518 | − | 0.988146i | \(-0.450940\pi\) | ||||
0.153518 | + | 0.988146i | \(0.450940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4250.77 | 0.178088 | 0.0890442 | − | 0.996028i | \(-0.471619\pi\) | ||||
0.0890442 | + | 0.996028i | \(0.471619\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17510.1 | 0.730949 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10149.9 | 0.420663 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12105.1 | 0.499895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39527.7 | 1.62652 | 0.813258 | − | 0.581903i | \(-0.197692\pi\) | ||||
0.813258 | + | 0.581903i | \(0.197692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24315.7 | −0.996993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24750.7 | −1.01122 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13142.8 | 0.535059 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12742.7 | 0.515109 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3464.76 | −0.139566 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31656.1 | 1.27067 | 0.635337 | − | 0.772235i | \(-0.280861\pi\) | ||||
0.635337 | + | 0.772235i | \(0.280861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17839.6 | 0.713568 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1193.16 | 0.0475583 | 0.0237792 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237792 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29060.0 | −1.15427 | −0.577134 | − | 0.816650i | \(-0.695829\pi\) | ||||
−0.577134 | + | 0.816650i | \(0.695829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23063.0 | −0.909702 | −0.454851 | − | 0.890567i | \(-0.650308\pi\) | ||||
−0.454851 | + | 0.890567i | \(0.650308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25059.4 | 0.985024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32029.2 | −1.25463 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −829.371 | −0.0323757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27698.2 | 1.07752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7803.54 | −0.302531 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33871.0 | 1.30415 | 0.652077 | − | 0.758153i | \(-0.273898\pi\) | ||||
0.652077 | + | 0.758153i | \(0.273898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11759.2 | −0.451228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43331.1 | −1.65705 | −0.828525 | − | 0.559953i | \(-0.810819\pi\) | ||||
−0.828525 | + | 0.559953i | \(0.810819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40897.3 | 1.55867 | 0.779334 | − | 0.626609i | \(-0.215558\pi\) | ||||
0.779334 | + | 0.626609i | \(0.215558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4544.23 | 0.172602 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45065.8 | 1.70593 | 0.852965 | − | 0.521968i | \(-0.174802\pi\) | ||||
0.852965 | + | 0.521968i | \(0.174802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 117.668 | 0.00442427 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31556.8 | −1.18254 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7047.19 | −0.263197 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15046.6 | 0.560078 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 703.180 | 0.0260872 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17556.3 | 0.649150 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39107.9 | −1.43645 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25282.5 | −0.925570 | −0.462785 | − | 0.886471i | \(-0.653150\pi\) | ||||
−0.462785 | + | 0.886471i | \(0.653150\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 932.311 | 0.0340185 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41646.1 | 1.51460 | 0.757298 | − | 0.653070i | \(-0.226519\pi\) | ||||
0.757298 | + | 0.653070i | \(0.226519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −84.7812 | −0.00307322 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5815.19 | −0.210103 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26112.5 | 0.937292 | 0.468646 | − | 0.883386i | \(-0.344742\pi\) | ||||
0.468646 | + | 0.883386i | \(0.344742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32554.8 | −1.16473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15699.9 | −0.559879 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1633.27 | 0.0580559 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25952.6 | 0.919519 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32357.0 | 1.14273 | 0.571366 | − | 0.820695i | \(-0.306414\pi\) | ||||
0.571366 | + | 0.820695i | \(0.306414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29220.1 | −1.02532 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1290.52 | 0.0451386 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32947.0 | 1.14870 | 0.574350 | − | 0.818610i | \(-0.305255\pi\) | ||||
0.574350 | + | 0.818610i | \(0.305255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10665.7 | −0.370673 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −501.602 | −0.0173770 | −0.00868849 | − | 0.999962i | \(-0.502766\pi\) | ||||
−0.00868849 | + | 0.999962i | \(0.502766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8481.06 | 0.292875 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6436.90 | 0.220878 | 0.110439 | − | 0.993883i | \(-0.464774\pi\) | ||||
0.110439 | + | 0.993883i | \(0.464774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16409.2 | −0.561292 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13917.7 | 0.474566 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47511.2 | 1.61494 | 0.807470 | − | 0.589908i | \(-0.200836\pi\) | ||||
0.807470 | + | 0.589908i | \(0.200836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35104.2 | 1.18947 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.9303 | 0.000842092 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23049.4 | −0.773705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12220.2 | 0.408919 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9115.15 | −0.304069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7817.32 | −0.259967 | −0.129984 | − | 0.991516i | \(-0.541492\pi\) | ||||
−0.129984 | + | 0.991516i | \(0.541492\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39315.6 | −1.30340 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1503.50 | −0.0496905 | −0.0248453 | − | 0.999691i | \(-0.507909\pi\) | ||||
−0.0248453 | + | 0.999691i | \(0.507909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7092.88 | −0.232978 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33389.1 | 1.09336 | 0.546680 | − | 0.837342i | \(-0.315892\pi\) | ||||
0.546680 | + | 0.837342i | \(0.315892\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1279.14 | 0.0417584 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22989.9 | 0.748228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5451.02 | 0.176867 | 0.0884337 | − | 0.996082i | \(-0.471814\pi\) | ||||
0.0884337 | + | 0.996082i | \(0.471814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49683.7 | 1.60716 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50165.4 | 1.61291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46530.0 | 1.49150 | 0.745750 | − | 0.666226i | \(-0.232092\pi\) | ||||
0.745750 | + | 0.666226i | \(0.232092\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17514.9 | −0.559736 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10780.6 | −0.343484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11410.0 | 0.362444 | 0.181222 | − | 0.983442i | \(-0.441995\pi\) | ||||
0.181222 | + | 0.983442i | \(0.441995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4247.95 | 0.134534 |
(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.bf.1.2 | 4 | ||
4.3 | odd | 2 | 49.4.a.e.1.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 784.4.a.bf.1.3 | 4 | ||
12.11 | even | 2 | 441.4.a.u.1.2 | 4 | |||
20.19 | odd | 2 | 1225.4.a.bb.1.1 | 4 | |||
28.3 | even | 6 | 49.4.c.e.30.2 | 8 | |||
28.11 | odd | 6 | 49.4.c.e.30.1 | 8 | |||
28.19 | even | 6 | 49.4.c.e.18.2 | 8 | |||
28.23 | odd | 6 | 49.4.c.e.18.1 | 8 | |||
28.27 | even | 2 | 49.4.a.e.1.3 | ✓ | 4 | ||
84.11 | even | 6 | 441.4.e.y.226.3 | 8 | |||
84.23 | even | 6 | 441.4.e.y.361.3 | 8 | |||
84.47 | odd | 6 | 441.4.e.y.361.4 | 8 | |||
84.59 | odd | 6 | 441.4.e.y.226.4 | 8 | |||
84.83 | odd | 2 | 441.4.a.u.1.1 | 4 | |||
140.139 | even | 2 | 1225.4.a.bb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.e.1.3 | ✓ | 4 | 28.27 | even | 2 | ||
49.4.a.e.1.4 | yes | 4 | 4.3 | odd | 2 | ||
49.4.c.e.18.1 | 8 | 28.23 | odd | 6 | |||
49.4.c.e.18.2 | 8 | 28.19 | even | 6 | |||
49.4.c.e.30.1 | 8 | 28.11 | odd | 6 | |||
49.4.c.e.30.2 | 8 | 28.3 | even | 6 | |||
441.4.a.u.1.1 | 4 | 84.83 | odd | 2 | |||
441.4.a.u.1.2 | 4 | 12.11 | even | 2 | |||
441.4.e.y.226.3 | 8 | 84.11 | even | 6 | |||
441.4.e.y.226.4 | 8 | 84.59 | odd | 6 | |||
441.4.e.y.361.3 | 8 | 84.23 | even | 6 | |||
441.4.e.y.361.4 | 8 | 84.47 | odd | 6 | |||
784.4.a.bf.1.2 | 4 | 1.1 | even | 1 | trivial | ||
784.4.a.bf.1.3 | 4 | 7.6 | odd | 2 | inner | ||
1225.4.a.bb.1.1 | 4 | 20.19 | odd | 2 | |||
1225.4.a.bb.1.2 | 4 | 140.139 | even | 2 |