Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,4,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.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: | \(24.4267907424\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 219x^{2} - 468x + 3240 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.93708\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −19.0098 | −1.70029 | −0.850145 | − | 0.526548i | \(-0.823486\pi\) | ||||
−0.850145 | + | 0.526548i | \(0.823486\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.4014 | −1.42554 | −0.712770 | − | 0.701397i | \(-0.752560\pi\) | ||||
−0.712770 | + | 0.701397i | \(0.752560\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −38.0197 | −1.20229 | ||||||||
\(11\) | 27.2657 | 0.747357 | 0.373678 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373678 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 69.8938 | 1.49116 | 0.745579 | − | 0.666417i | \(-0.232173\pi\) | ||||
0.745579 | + | 0.666417i | \(0.232173\pi\) | |||||||
\(14\) | −52.8028 | −1.00801 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −15.2407 | −0.217437 | −0.108718 | − | 0.994073i | \(-0.534675\pi\) | ||||
−0.108718 | + | 0.994073i | \(0.534675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 65.6587 | 0.792797 | 0.396398 | − | 0.918079i | \(-0.370260\pi\) | ||||
0.396398 | + | 0.918079i | \(0.370260\pi\) | |||||||
\(20\) | −76.0393 | −0.850145 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 54.5314 | 0.528461 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 236.374 | 1.89099 | ||||||||
\(26\) | 139.788 | 1.05441 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −105.606 | −0.712770 | ||||||||
\(29\) | 124.619 | 0.797968 | 0.398984 | − | 0.916958i | \(-0.369363\pi\) | ||||
0.398984 | + | 0.916958i | \(0.369363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 302.744 | 1.75402 | 0.877008 | − | 0.480476i | \(-0.159536\pi\) | ||||
0.877008 | + | 0.480476i | \(0.159536\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −30.4815 | −0.153751 | ||||||||
\(35\) | 501.886 | 2.42383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.93992 | 0.0263924 | 0.0131962 | − | 0.999913i | \(-0.495799\pi\) | ||||
0.0131962 | + | 0.999913i | \(0.495799\pi\) | |||||||
\(38\) | 131.317 | 0.560592 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −152.079 | −0.601144 | ||||||||
\(41\) | −166.526 | −0.634316 | −0.317158 | − | 0.948373i | \(-0.602729\pi\) | ||||
−0.317158 | + | 0.948373i | \(0.602729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −318.295 | −1.12882 | −0.564412 | − | 0.825493i | \(-0.690897\pi\) | ||||
−0.564412 | + | 0.825493i | \(0.690897\pi\) | |||||||
\(44\) | 109.063 | 0.373678 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 144.643 | 0.448902 | 0.224451 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224451 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 354.033 | 1.03217 | ||||||||
\(50\) | 472.747 | 1.33713 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 279.575 | 0.745579 | ||||||||
\(53\) | −502.487 | −1.30230 | −0.651150 | − | 0.758949i | \(-0.725713\pi\) | ||||
−0.651150 | + | 0.758949i | \(0.725713\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −518.317 | −1.27072 | ||||||||
\(56\) | −211.211 | −0.504005 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 249.237 | 0.564249 | ||||||||
\(59\) | −600.540 | −1.32515 | −0.662573 | − | 0.748997i | \(-0.730536\pi\) | ||||
−0.662573 | + | 0.748997i | \(0.730536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 636.071 | 1.33509 | 0.667546 | − | 0.744569i | \(-0.267345\pi\) | ||||
0.667546 | + | 0.744569i | \(0.267345\pi\) | |||||||
\(62\) | 605.489 | 1.24028 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1328.67 | −2.53540 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 206.163 | 0.375922 | 0.187961 | − | 0.982176i | \(-0.439812\pi\) | ||||
0.187961 | + | 0.982176i | \(0.439812\pi\) | |||||||
\(68\) | −60.9630 | −0.108718 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1003.77 | 1.71391 | ||||||||
\(71\) | 440.948 | 0.737055 | 0.368527 | − | 0.929617i | \(-0.379862\pi\) | ||||
0.368527 | + | 0.929617i | \(0.379862\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 390.246 | 0.625683 | 0.312841 | − | 0.949805i | \(-0.398719\pi\) | ||||
0.312841 | + | 0.949805i | \(0.398719\pi\) | |||||||
\(74\) | 11.8798 | 0.0186622 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 262.635 | 0.396398 | ||||||||
\(77\) | −719.853 | −1.06539 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 681.317 | 0.970306 | 0.485153 | − | 0.874429i | \(-0.338764\pi\) | ||||
0.485153 | + | 0.874429i | \(0.338764\pi\) | |||||||
\(80\) | −304.157 | −0.425073 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −333.051 | −0.448529 | ||||||||
\(83\) | −695.269 | −0.919466 | −0.459733 | − | 0.888057i | \(-0.652055\pi\) | ||||
−0.459733 | + | 0.888057i | \(0.652055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 289.724 | 0.369705 | ||||||||
\(86\) | −636.589 | −0.798200 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 218.126 | 0.264230 | ||||||||
\(89\) | 948.900 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1845.29 | −2.12571 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 289.286 | 0.317421 | ||||||||
\(95\) | −1248.16 | −1.34798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 746.861 | 0.781775 | 0.390888 | − | 0.920438i | \(-0.372168\pi\) | ||||
0.390888 | + | 0.920438i | \(0.372168\pi\) | |||||||
\(98\) | 708.067 | 0.729852 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 945.494 | 0.945494 | ||||||||
\(101\) | 1168.00 | 1.15070 | 0.575349 | − | 0.817908i | \(-0.304866\pi\) | ||||
0.575349 | + | 0.817908i | \(0.304866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 608.376 | 0.581991 | 0.290995 | − | 0.956724i | \(-0.406014\pi\) | ||||
0.290995 | + | 0.956724i | \(0.406014\pi\) | |||||||
\(104\) | 559.150 | 0.527204 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1004.97 | −0.920866 | ||||||||
\(107\) | 1134.79 | 1.02528 | 0.512638 | − | 0.858605i | \(-0.328668\pi\) | ||||
0.512638 | + | 0.858605i | \(0.328668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1602.61 | 1.40828 | 0.704140 | − | 0.710061i | \(-0.251333\pi\) | ||||
0.704140 | + | 0.710061i | \(0.251333\pi\) | |||||||
\(110\) | −1036.63 | −0.898537 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −422.422 | −0.356385 | ||||||||
\(113\) | −2049.37 | −1.70609 | −0.853046 | − | 0.521836i | \(-0.825247\pi\) | ||||
−0.853046 | + | 0.521836i | \(0.825247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −437.226 | −0.354535 | ||||||||
\(116\) | 498.474 | 0.398984 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1201.08 | −0.937020 | ||||||||
\(119\) | 402.377 | 0.309965 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −587.581 | −0.441458 | ||||||||
\(122\) | 1272.14 | 0.944052 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1210.98 | 0.877008 | ||||||||
\(125\) | −2117.19 | −1.51494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1322.84 | 0.924278 | 0.462139 | − | 0.886807i | \(-0.347082\pi\) | ||||
0.462139 | + | 0.886807i | \(0.347082\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2657.34 | −1.79280 | ||||||||
\(131\) | 353.591 | 0.235827 | 0.117914 | − | 0.993024i | \(-0.462379\pi\) | ||||
0.117914 | + | 0.993024i | \(0.462379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1733.48 | −1.13016 | ||||||||
\(134\) | 412.326 | 0.265817 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −121.926 | −0.0768755 | ||||||||
\(137\) | 3171.79 | 1.97799 | 0.988995 | − | 0.147948i | \(-0.0472670\pi\) | ||||
0.988995 | + | 0.147948i | \(0.0472670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 508.055 | 0.310019 | 0.155010 | − | 0.987913i | \(-0.450459\pi\) | ||||
0.155010 | + | 0.987913i | \(0.450459\pi\) | |||||||
\(140\) | 2007.54 | 1.21192 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 881.896 | 0.521176 | ||||||||
\(143\) | 1905.71 | 1.11443 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2368.98 | −1.35678 | ||||||||
\(146\) | 780.492 | 0.442424 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.7597 | 0.0131962 | ||||||||
\(149\) | −2954.62 | −1.62451 | −0.812255 | − | 0.583303i | \(-0.801760\pi\) | ||||
−0.812255 | + | 0.583303i | \(0.801760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3383.54 | −1.82350 | −0.911749 | − | 0.410747i | \(-0.865268\pi\) | ||||
−0.911749 | + | 0.410747i | \(0.865268\pi\) | |||||||
\(152\) | 525.270 | 0.280296 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1439.71 | −0.753343 | ||||||||
\(155\) | −5755.12 | −2.98234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −293.879 | −0.149389 | −0.0746945 | − | 0.997206i | \(-0.523798\pi\) | ||||
−0.0746945 | + | 0.997206i | \(0.523798\pi\) | |||||||
\(158\) | 1362.63 | 0.686110 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −608.314 | −0.300572 | ||||||||
\(161\) | −607.232 | −0.297246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1277.17 | 0.613717 | 0.306859 | − | 0.951755i | \(-0.400722\pi\) | ||||
0.306859 | + | 0.951755i | \(0.400722\pi\) | |||||||
\(164\) | −666.103 | −0.317158 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1390.54 | −0.650161 | ||||||||
\(167\) | 1509.84 | 0.699609 | 0.349805 | − | 0.936823i | \(-0.386248\pi\) | ||||
0.349805 | + | 0.936823i | \(0.386248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2688.15 | 1.22355 | ||||||||
\(170\) | 579.448 | 0.261421 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1273.18 | −0.564412 | ||||||||
\(173\) | 137.777 | 0.0605490 | 0.0302745 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302745 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6240.59 | −2.69568 | ||||||||
\(176\) | 436.252 | 0.186839 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1897.80 | 0.799135 | ||||||||
\(179\) | −3043.97 | −1.27105 | −0.635523 | − | 0.772082i | \(-0.719216\pi\) | ||||
−0.635523 | + | 0.772082i | \(0.719216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3906.90 | 1.60441 | 0.802204 | − | 0.597051i | \(-0.203661\pi\) | ||||
0.802204 | + | 0.597051i | \(0.203661\pi\) | |||||||
\(182\) | −3690.59 | −1.50310 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −112.917 | −0.0448747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −415.550 | −0.162503 | ||||||||
\(188\) | 578.573 | 0.224451 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2496.32 | −0.953169 | ||||||||
\(191\) | 1018.93 | 0.386007 | 0.193004 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193004 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4302.92 | −1.60482 | −0.802412 | − | 0.596771i | \(-0.796450\pi\) | ||||
−0.802412 | + | 0.596771i | \(0.796450\pi\) | |||||||
\(194\) | 1493.72 | 0.552799 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1416.13 | 0.516083 | ||||||||
\(197\) | 1439.36 | 0.520558 | 0.260279 | − | 0.965533i | \(-0.416185\pi\) | ||||
0.260279 | + | 0.965533i | \(0.416185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5262.93 | 1.87477 | 0.937385 | − | 0.348295i | \(-0.113239\pi\) | ||||
0.937385 | + | 0.348295i | \(0.113239\pi\) | |||||||
\(200\) | 1890.99 | 0.668565 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2336.00 | 0.813666 | ||||||||
\(203\) | −3290.10 | −1.13754 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3165.63 | 1.07852 | ||||||||
\(206\) | 1216.75 | 0.411530 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1118.30 | 0.372790 | ||||||||
\(209\) | 1790.23 | 0.592502 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 353.694 | 0.115399 | 0.0576997 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0576997 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(212\) | −2009.95 | −0.651150 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2269.58 | 0.724979 | ||||||||
\(215\) | 6050.73 | 1.91933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7992.87 | −2.50042 | ||||||||
\(218\) | 3205.23 | 0.995804 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2073.27 | −0.635362 | ||||||||
\(221\) | −1065.23 | −0.324232 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5336.31 | −1.60245 | −0.801223 | − | 0.598366i | \(-0.795817\pi\) | ||||
−0.801223 | + | 0.598366i | \(0.795817\pi\) | |||||||
\(224\) | −844.844 | −0.252002 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4098.74 | −1.20639 | ||||||||
\(227\) | 2213.30 | 0.647144 | 0.323572 | − | 0.946204i | \(-0.395116\pi\) | ||||
0.323572 | + | 0.946204i | \(0.395116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5141.09 | −1.48355 | −0.741774 | − | 0.670650i | \(-0.766015\pi\) | ||||
−0.741774 | + | 0.670650i | \(0.766015\pi\) | |||||||
\(230\) | −874.452 | −0.250694 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 996.948 | 0.282124 | ||||||||
\(233\) | 6582.34 | 1.85074 | 0.925372 | − | 0.379061i | \(-0.123753\pi\) | ||||
0.925372 | + | 0.379061i | \(0.123753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2749.64 | −0.763263 | ||||||||
\(236\) | −2402.16 | −0.662573 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 804.753 | 0.219178 | ||||||||
\(239\) | 6205.96 | 1.67962 | 0.839812 | − | 0.542877i | \(-0.182665\pi\) | ||||
0.839812 | + | 0.542877i | \(0.182665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6363.48 | −1.70086 | −0.850432 | − | 0.526086i | \(-0.823659\pi\) | ||||
−0.850432 | + | 0.526086i | \(0.823659\pi\) | |||||||
\(242\) | −1175.16 | −0.312158 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2544.28 | 0.667546 | ||||||||
\(245\) | −6730.11 | −1.75498 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4589.14 | 1.18219 | ||||||||
\(248\) | 2421.95 | 0.620138 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4234.38 | −1.07122 | ||||||||
\(251\) | 1761.97 | 0.443087 | 0.221544 | − | 0.975150i | \(-0.428891\pi\) | ||||
0.221544 | + | 0.975150i | \(0.428891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 627.112 | 0.155835 | ||||||||
\(254\) | 2645.69 | 0.653563 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −446.547 | −0.108385 | −0.0541923 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541923 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −156.822 | −0.0376234 | ||||||||
\(260\) | −5314.68 | −1.26770 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 707.182 | 0.166755 | ||||||||
\(263\) | −8390.91 | −1.96732 | −0.983661 | − | 0.180033i | \(-0.942379\pi\) | ||||
−0.983661 | + | 0.180033i | \(0.942379\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9552.20 | 2.21429 | ||||||||
\(266\) | −3466.96 | −0.799147 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 824.651 | 0.187961 | ||||||||
\(269\) | −4219.17 | −0.956310 | −0.478155 | − | 0.878275i | \(-0.658694\pi\) | ||||
−0.478155 | + | 0.878275i | \(0.658694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4711.39 | 1.05608 | 0.528038 | − | 0.849221i | \(-0.322928\pi\) | ||||
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(272\) | −243.852 | −0.0543592 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6343.59 | 1.39865 | ||||||||
\(275\) | 6444.89 | 1.41324 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6017.91 | −1.30535 | −0.652674 | − | 0.757639i | \(-0.726353\pi\) | ||||
−0.652674 | + | 0.757639i | \(0.726353\pi\) | |||||||
\(278\) | 1016.11 | 0.219217 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4015.09 | 0.856955 | ||||||||
\(281\) | −5210.98 | −1.10627 | −0.553134 | − | 0.833092i | \(-0.686568\pi\) | ||||
−0.553134 | + | 0.833092i | \(0.686568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5156.61 | −1.08314 | −0.541570 | − | 0.840655i | \(-0.682170\pi\) | ||||
−0.541570 | + | 0.840655i | \(0.682170\pi\) | |||||||
\(284\) | 1763.79 | 0.368527 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3811.41 | 0.788019 | ||||||||
\(287\) | 4396.51 | 0.904243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4680.72 | −0.952721 | ||||||||
\(290\) | −4737.95 | −0.959387 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1560.98 | 0.312841 | ||||||||
\(293\) | 4978.19 | 0.992590 | 0.496295 | − | 0.868154i | \(-0.334693\pi\) | ||||
0.496295 | + | 0.868154i | \(0.334693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11416.2 | 2.25313 | ||||||||
\(296\) | 47.5194 | 0.00933111 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5909.24 | −1.14870 | ||||||||
\(299\) | 1607.56 | 0.310928 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8403.42 | 1.60919 | ||||||||
\(302\) | −6767.07 | −1.28941 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1050.54 | 0.198199 | ||||||||
\(305\) | −12091.6 | −2.27004 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3035.93 | 0.564396 | 0.282198 | − | 0.959356i | \(-0.408937\pi\) | ||||
0.282198 | + | 0.959356i | \(0.408937\pi\) | |||||||
\(308\) | −2879.41 | −0.532694 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11510.2 | −2.10883 | ||||||||
\(311\) | 4811.62 | 0.877305 | 0.438652 | − | 0.898657i | \(-0.355456\pi\) | ||||
0.438652 | + | 0.898657i | \(0.355456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6959.90 | −1.25686 | −0.628429 | − | 0.777867i | \(-0.716302\pi\) | ||||
−0.628429 | + | 0.777867i | \(0.716302\pi\) | |||||||
\(314\) | −587.758 | −0.105634 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2725.27 | 0.485153 | ||||||||
\(317\) | −2817.16 | −0.499140 | −0.249570 | − | 0.968357i | \(-0.580289\pi\) | ||||
−0.249570 | + | 0.968357i | \(0.580289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3397.81 | 0.596367 | ||||||||
\(320\) | −1216.63 | −0.212536 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1214.46 | −0.210185 | ||||||||
\(323\) | −1000.69 | −0.172383 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16521.0 | 2.81976 | ||||||||
\(326\) | 2554.35 | 0.433964 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1332.21 | −0.224265 | ||||||||
\(329\) | −3818.78 | −0.639928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8262.04 | 1.37197 | 0.685986 | − | 0.727614i | \(-0.259371\pi\) | ||||
0.685986 | + | 0.727614i | \(0.259371\pi\) | |||||||
\(332\) | −2781.08 | −0.459733 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3019.68 | 0.494699 | ||||||||
\(335\) | −3919.12 | −0.639177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8303.24 | −1.34215 | −0.671077 | − | 0.741387i | \(-0.734168\pi\) | ||||
−0.671077 | + | 0.741387i | \(0.734168\pi\) | |||||||
\(338\) | 5376.29 | 0.865182 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1158.90 | 0.184853 | ||||||||
\(341\) | 8254.54 | 1.31088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −291.293 | −0.0458553 | ||||||||
\(344\) | −2546.36 | −0.399100 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 275.554 | 0.0428146 | ||||||||
\(347\) | −307.537 | −0.0475776 | −0.0237888 | − | 0.999717i | \(-0.507573\pi\) | ||||
−0.0237888 | + | 0.999717i | \(0.507573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9250 | −0.00167564 | −0.000837822 | − | 1.00000i | \(-0.500267\pi\) | ||||
−0.000837822 | 1.00000i | \(0.500267\pi\) | ||||||||
\(350\) | −12481.2 | −1.90613 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 872.503 | 0.132115 | ||||||||
\(353\) | −525.894 | −0.0792932 | −0.0396466 | − | 0.999214i | \(-0.512623\pi\) | ||||
−0.0396466 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8382.34 | −1.25321 | ||||||||
\(356\) | 3795.60 | 0.565074 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6087.95 | −0.898766 | ||||||||
\(359\) | −1726.99 | −0.253891 | −0.126946 | − | 0.991910i | \(-0.540517\pi\) | ||||
−0.126946 | + | 0.991910i | \(0.540517\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2547.94 | −0.371473 | ||||||||
\(362\) | 7813.80 | 1.13449 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7381.17 | −1.06285 | ||||||||
\(365\) | −7418.51 | −1.06384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −537.816 | −0.0764953 | −0.0382477 | − | 0.999268i | \(-0.512178\pi\) | ||||
−0.0382477 | + | 0.999268i | \(0.512178\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −225.834 | −0.0317312 | ||||||||
\(371\) | 13266.4 | 1.85648 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3074.20 | 0.426745 | 0.213373 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213373 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(374\) | −831.100 | −0.114907 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1157.15 | 0.158711 | ||||||||
\(377\) | 8710.07 | 1.18990 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9245.15 | 1.25301 | 0.626506 | − | 0.779417i | \(-0.284485\pi\) | ||||
0.626506 | + | 0.779417i | \(0.284485\pi\) | |||||||
\(380\) | −4992.64 | −0.673992 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2037.87 | 0.272948 | ||||||||
\(383\) | 2029.45 | 0.270758 | 0.135379 | − | 0.990794i | \(-0.456775\pi\) | ||||
0.135379 | + | 0.990794i | \(0.456775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13684.3 | 1.81147 | ||||||||
\(386\) | −8605.84 | −1.13478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2987.44 | 0.390888 | ||||||||
\(389\) | 7081.67 | 0.923020 | 0.461510 | − | 0.887135i | \(-0.347308\pi\) | ||||
0.461510 | + | 0.887135i | \(0.347308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −350.537 | −0.0453387 | ||||||||
\(392\) | 2832.27 | 0.364926 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2878.71 | 0.368090 | ||||||||
\(395\) | −12951.7 | −1.64980 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3974.11 | 0.502405 | 0.251203 | − | 0.967935i | \(-0.419174\pi\) | ||||
0.251203 | + | 0.967935i | \(0.419174\pi\) | |||||||
\(398\) | 10525.9 | 1.32566 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3781.98 | 0.472747 | ||||||||
\(401\) | −1228.32 | −0.152966 | −0.0764830 | − | 0.997071i | \(-0.524369\pi\) | ||||
−0.0764830 | + | 0.997071i | \(0.524369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21160.0 | 2.61551 | ||||||||
\(404\) | 4672.01 | 0.575349 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6580.21 | −0.804360 | ||||||||
\(407\) | 161.956 | 0.0197245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4559.87 | −0.551274 | −0.275637 | − | 0.961262i | \(-0.588889\pi\) | ||||
−0.275637 | + | 0.961262i | \(0.588889\pi\) | |||||||
\(410\) | 6331.25 | 0.762630 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2433.50 | 0.290995 | ||||||||
\(413\) | 15855.1 | 1.88905 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13216.9 | 1.56336 | ||||||||
\(416\) | 2236.60 | 0.263602 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3580.46 | 0.418962 | ||||||||
\(419\) | 16364.6 | 1.90803 | 0.954013 | − | 0.299766i | \(-0.0969084\pi\) | ||||
0.954013 | + | 0.299766i | \(0.0969084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8467.50 | 0.980239 | 0.490120 | − | 0.871655i | \(-0.336953\pi\) | ||||
0.490120 | + | 0.871655i | \(0.336953\pi\) | |||||||
\(422\) | 707.387 | 0.0815997 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4019.90 | −0.460433 | ||||||||
\(425\) | −3602.51 | −0.411170 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16793.2 | −1.90323 | ||||||||
\(428\) | 4539.17 | 0.512638 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12101.5 | 1.35717 | ||||||||
\(431\) | 12440.5 | 1.39034 | 0.695172 | − | 0.718843i | \(-0.255328\pi\) | ||||
0.695172 | + | 0.718843i | \(0.255328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4079.23 | 0.452737 | 0.226369 | − | 0.974042i | \(-0.427315\pi\) | ||||
0.226369 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(434\) | −15985.7 | −1.76806 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6410.45 | 0.704140 | ||||||||
\(437\) | 1510.15 | 0.165310 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3486.22 | 0.379017 | 0.189508 | − | 0.981879i | \(-0.439311\pi\) | ||||
0.189508 | + | 0.981879i | \(0.439311\pi\) | |||||||
\(440\) | −4146.53 | −0.449269 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2130.47 | −0.229267 | ||||||||
\(443\) | 11320.3 | 1.21409 | 0.607047 | − | 0.794666i | \(-0.292354\pi\) | ||||
0.607047 | + | 0.794666i | \(0.292354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18038.4 | −1.92158 | ||||||||
\(446\) | −10672.6 | −1.13310 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1689.69 | −0.178193 | ||||||||
\(449\) | −16854.6 | −1.77154 | −0.885768 | − | 0.464129i | \(-0.846367\pi\) | ||||
−0.885768 | + | 0.464129i | \(0.846367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4540.44 | −0.474060 | ||||||||
\(452\) | −8197.47 | −0.853046 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4426.59 | 0.457600 | ||||||||
\(455\) | 35078.7 | 3.61432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5329.53 | −0.545525 | −0.272762 | − | 0.962081i | \(-0.587937\pi\) | ||||
−0.272762 | + | 0.962081i | \(0.587937\pi\) | |||||||
\(458\) | −10282.2 | −1.04903 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1748.90 | −0.177268 | ||||||||
\(461\) | 8612.31 | 0.870098 | 0.435049 | − | 0.900407i | \(-0.356731\pi\) | ||||
0.435049 | + | 0.900407i | \(0.356731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11553.9 | −1.15973 | −0.579867 | − | 0.814711i | \(-0.696896\pi\) | ||||
−0.579867 | + | 0.814711i | \(0.696896\pi\) | |||||||
\(464\) | 1993.90 | 0.199492 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13164.7 | 1.30867 | ||||||||
\(467\) | 6425.53 | 0.636698 | 0.318349 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318349 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5442.98 | −0.535893 | ||||||||
\(470\) | −5499.28 | −0.539709 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4804.32 | −0.468510 | ||||||||
\(473\) | −8678.53 | −0.843635 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15520.0 | 1.49917 | ||||||||
\(476\) | 1609.51 | 0.154982 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12411.9 | 1.18767 | ||||||||
\(479\) | 8666.10 | 0.826647 | 0.413324 | − | 0.910584i | \(-0.364368\pi\) | ||||
0.413324 | + | 0.910584i | \(0.364368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 415.164 | 0.0393552 | ||||||||
\(482\) | −12727.0 | −1.20269 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2350.32 | −0.220729 | ||||||||
\(485\) | −14197.7 | −1.32925 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18563.6 | −1.72730 | −0.863652 | − | 0.504088i | \(-0.831829\pi\) | ||||
−0.863652 | + | 0.504088i | \(0.831829\pi\) | |||||||
\(488\) | 5088.57 | 0.472026 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13460.2 | −1.24096 | ||||||||
\(491\) | −11797.2 | −1.08432 | −0.542161 | − | 0.840274i | \(-0.682394\pi\) | ||||
−0.542161 | + | 0.840274i | \(0.682394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1899.28 | −0.173508 | ||||||||
\(494\) | 9178.27 | 0.835931 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4843.91 | 0.438504 | ||||||||
\(497\) | −11641.6 | −1.05070 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3453.29 | −0.309801 | −0.154900 | − | 0.987930i | \(-0.549506\pi\) | ||||
−0.154900 | + | 0.987930i | \(0.549506\pi\) | |||||||
\(500\) | −8468.77 | −0.757469 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3523.95 | 0.313310 | ||||||||
\(503\) | 9326.34 | 0.826721 | 0.413361 | − | 0.910567i | \(-0.364355\pi\) | ||||
0.413361 | + | 0.910567i | \(0.364355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22203.5 | −1.95652 | ||||||||
\(506\) | 1254.22 | 0.110192 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5291.37 | 0.462139 | ||||||||
\(509\) | −12603.6 | −1.09754 | −0.548768 | − | 0.835975i | \(-0.684903\pi\) | ||||
−0.548768 | + | 0.835975i | \(0.684903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10303.0 | −0.891936 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −893.094 | −0.0766394 | ||||||||
\(515\) | −11565.1 | −0.989554 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3943.80 | 0.335490 | ||||||||
\(518\) | −313.645 | −0.0266038 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10629.4 | −0.896400 | ||||||||
\(521\) | −17821.9 | −1.49864 | −0.749322 | − | 0.662206i | \(-0.769620\pi\) | ||||
−0.749322 | + | 0.662206i | \(0.769620\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3816.68 | −0.319104 | −0.159552 | − | 0.987189i | \(-0.551005\pi\) | ||||
−0.159552 | + | 0.987189i | \(0.551005\pi\) | |||||||
\(524\) | 1414.36 | 0.117914 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16781.8 | −1.39111 | ||||||||
\(527\) | −4614.05 | −0.381387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 19104.4 | 1.56574 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6933.92 | −0.565082 | ||||||||
\(533\) | −11639.1 | −0.945865 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21572.2 | −1.74327 | ||||||||
\(536\) | 1649.30 | 0.132909 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8438.34 | −0.676213 | ||||||||
\(539\) | 9652.97 | 0.771397 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12730.5 | 1.01169 | 0.505846 | − | 0.862624i | \(-0.331180\pi\) | ||||
0.505846 | + | 0.862624i | \(0.331180\pi\) | |||||||
\(542\) | 9422.78 | 0.746759 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −487.704 | −0.0384377 | ||||||||
\(545\) | −30465.4 | −2.39449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 175.554 | 0.0137224 | 0.00686119 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686119 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(548\) | 12687.2 | 0.988995 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12889.8 | 0.999313 | ||||||||
\(551\) | 8182.29 | 0.632627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17987.7 | −1.38321 | ||||||||
\(554\) | −12035.8 | −0.923020 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2032.22 | 0.155010 | ||||||||
\(557\) | 4603.34 | 0.350179 | 0.175089 | − | 0.984553i | \(-0.443979\pi\) | ||||
0.175089 | + | 0.984553i | \(0.443979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22246.8 | −1.68326 | ||||||||
\(560\) | 8030.17 | 0.605958 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10422.0 | −0.782249 | ||||||||
\(563\) | 3425.06 | 0.256393 | 0.128196 | − | 0.991749i | \(-0.459081\pi\) | ||||
0.128196 | + | 0.991749i | \(0.459081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38958.1 | 2.90085 | ||||||||
\(566\) | −10313.2 | −0.765896 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3527.58 | 0.260588 | ||||||||
\(569\) | −23899.8 | −1.76086 | −0.880431 | − | 0.474175i | \(-0.842746\pi\) | ||||
−0.880431 | + | 0.474175i | \(0.842746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12192.1 | −0.893563 | −0.446781 | − | 0.894643i | \(-0.647430\pi\) | ||||
−0.446781 | + | 0.894643i | \(0.647430\pi\) | |||||||
\(572\) | 7622.82 | 0.557214 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8793.02 | 0.639397 | ||||||||
\(575\) | 5436.59 | 0.394298 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16729.8 | 1.20706 | 0.603529 | − | 0.797341i | \(-0.293761\pi\) | ||||
0.603529 | + | 0.797341i | \(0.293761\pi\) | |||||||
\(578\) | −9361.44 | −0.673676 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9475.91 | −0.678389 | ||||||||
\(581\) | 18356.1 | 1.31074 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13700.7 | −0.973283 | ||||||||
\(584\) | 3121.97 | 0.221212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9956.38 | 0.701867 | ||||||||
\(587\) | 10502.3 | 0.738463 | 0.369231 | − | 0.929338i | \(-0.379621\pi\) | ||||
0.369231 | + | 0.929338i | \(0.379621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19877.8 | 1.39058 | ||||||||
\(590\) | 22832.3 | 1.59321 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 95.0388 | 0.00659809 | ||||||||
\(593\) | 19802.9 | 1.37134 | 0.685671 | − | 0.727912i | \(-0.259509\pi\) | ||||
0.685671 | + | 0.727912i | \(0.259509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7649.11 | −0.527030 | ||||||||
\(596\) | −11818.5 | −0.812255 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3215.12 | 0.219859 | ||||||||
\(599\) | −26702.7 | −1.82144 | −0.910720 | − | 0.413024i | \(-0.864472\pi\) | ||||
−0.910720 | + | 0.413024i | \(0.864472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18863.6 | −1.28030 | −0.640150 | − | 0.768250i | \(-0.721128\pi\) | ||||
−0.640150 | + | 0.768250i | \(0.721128\pi\) | |||||||
\(602\) | 16806.8 | 1.13787 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13534.1 | −0.911749 | ||||||||
\(605\) | 11169.8 | 0.750607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10095.7 | 0.675079 | 0.337539 | − | 0.941311i | \(-0.390405\pi\) | ||||
0.337539 | + | 0.941311i | \(0.390405\pi\) | |||||||
\(608\) | 2101.08 | 0.140148 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24183.2 | −1.60516 | ||||||||
\(611\) | 10109.7 | 0.669383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 770.460 | 0.0507644 | 0.0253822 | − | 0.999678i | \(-0.491920\pi\) | ||||
0.0253822 | + | 0.999678i | \(0.491920\pi\) | |||||||
\(614\) | 6071.85 | 0.399088 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5758.82 | −0.376671 | ||||||||
\(617\) | −6297.91 | −0.410931 | −0.205465 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205465 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 893.359 | 0.0580083 | 0.0290041 | − | 0.999579i | \(-0.490766\pi\) | ||||
0.0290041 | + | 0.999579i | \(0.490766\pi\) | |||||||
\(620\) | −23020.5 | −1.49117 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9623.23 | 0.620348 | ||||||||
\(623\) | −25052.3 | −1.61107 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10700.8 | 0.684848 | ||||||||
\(626\) | −13919.8 | −0.888733 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1175.52 | −0.0746945 | ||||||||
\(629\) | −90.5289 | −0.00573867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16031.2 | 1.01140 | 0.505698 | − | 0.862711i | \(-0.331235\pi\) | ||||
0.505698 | + | 0.862711i | \(0.331235\pi\) | |||||||
\(632\) | 5450.54 | 0.343055 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5634.31 | −0.352945 | ||||||||
\(635\) | −25147.0 | −1.57154 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24744.7 | 1.53912 | ||||||||
\(638\) | 6795.63 | 0.421695 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2433.26 | −0.150286 | ||||||||
\(641\) | 11366.2 | 0.700370 | 0.350185 | − | 0.936681i | \(-0.386119\pi\) | ||||
0.350185 | + | 0.936681i | \(0.386119\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −267.056 | −0.0163789 | −0.00818946 | − | 0.999966i | \(-0.502607\pi\) | ||||
−0.00818946 | + | 0.999966i | \(0.502607\pi\) | |||||||
\(644\) | −2428.93 | −0.148623 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2001.37 | −0.121893 | ||||||||
\(647\) | −10111.1 | −0.614389 | −0.307194 | − | 0.951647i | \(-0.599390\pi\) | ||||
−0.307194 | + | 0.951647i | \(0.599390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16374.1 | −0.990357 | ||||||||
\(650\) | 33042.1 | 1.99387 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5108.69 | 0.306859 | ||||||||
\(653\) | 12953.9 | 0.776299 | 0.388150 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388150 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6721.70 | −0.400975 | ||||||||
\(656\) | −2664.41 | −0.158579 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7637.56 | −0.452497 | ||||||||
\(659\) | −920.513 | −0.0544129 | −0.0272064 | − | 0.999630i | \(-0.508661\pi\) | ||||
−0.0272064 | + | 0.999630i | \(0.508661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6224.81 | 0.366289 | 0.183144 | − | 0.983086i | \(-0.441372\pi\) | ||||
0.183144 | + | 0.983086i | \(0.441372\pi\) | |||||||
\(662\) | 16524.1 | 0.970131 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5562.15 | −0.325080 | ||||||||
\(665\) | 32953.2 | 1.92161 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2866.23 | 0.166388 | ||||||||
\(668\) | 6039.35 | 0.349805 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7838.24 | −0.451966 | ||||||||
\(671\) | 17342.9 | 0.997789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7195.10 | 0.412111 | 0.206056 | − | 0.978540i | \(-0.433937\pi\) | ||||
0.206056 | + | 0.978540i | \(0.433937\pi\) | |||||||
\(674\) | −16606.5 | −0.949047 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10752.6 | 0.611776 | ||||||||
\(677\) | −2584.01 | −0.146694 | −0.0733468 | − | 0.997306i | \(-0.523368\pi\) | ||||
−0.0733468 | + | 0.997306i | \(0.523368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19718.2 | −1.11445 | ||||||||
\(680\) | 2317.79 | 0.130711 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16509.1 | 0.926929 | ||||||||
\(683\) | −15445.0 | −0.865280 | −0.432640 | − | 0.901567i | \(-0.642418\pi\) | ||||
−0.432640 | + | 0.901567i | \(0.642418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −60295.3 | −3.36316 | ||||||||
\(686\) | −582.587 | −0.0324246 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5092.71 | −0.282206 | ||||||||
\(689\) | −35120.7 | −1.94194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28002.8 | 1.54164 | 0.770822 | − | 0.637050i | \(-0.219846\pi\) | ||||
0.770822 | + | 0.637050i | \(0.219846\pi\) | |||||||
\(692\) | 551.107 | 0.0302745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −615.074 | −0.0336425 | ||||||||
\(695\) | −9658.05 | −0.527123 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2537.98 | 0.137924 | ||||||||
\(698\) | −21.8499 | −0.00118486 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24962.4 | −1.34784 | ||||||||
\(701\) | −31379.7 | −1.69072 | −0.845360 | − | 0.534198i | \(-0.820614\pi\) | ||||
−0.845360 | + | 0.534198i | \(0.820614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 390.008 | 0.0209238 | ||||||||
\(704\) | 1745.01 | 0.0934196 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1051.79 | −0.0560688 | ||||||||
\(707\) | −30836.9 | −1.64037 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12612.6 | −0.668092 | −0.334046 | − | 0.942557i | \(-0.608414\pi\) | ||||
−0.334046 | + | 0.942557i | \(0.608414\pi\) | |||||||
\(710\) | −16764.7 | −0.886151 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7591.20 | 0.399568 | ||||||||
\(713\) | 6963.12 | 0.365738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36227.1 | −1.89485 | ||||||||
\(716\) | −12175.9 | −0.635523 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3453.98 | −0.179528 | ||||||||
\(719\) | −8522.72 | −0.442064 | −0.221032 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221032 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16062.0 | −0.829652 | ||||||||
\(722\) | −5095.87 | −0.262671 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15627.6 | 0.802204 | ||||||||
\(725\) | 29456.5 | 1.50895 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9853.76 | 0.502690 | 0.251345 | − | 0.967898i | \(-0.419127\pi\) | ||||
0.251345 | + | 0.967898i | \(0.419127\pi\) | |||||||
\(728\) | −14762.3 | −0.751551 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14837.0 | −0.752250 | ||||||||
\(731\) | 4851.05 | 0.245448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21851.1 | −1.10107 | −0.550537 | − | 0.834810i | \(-0.685577\pi\) | ||||
−0.550537 | + | 0.834810i | \(0.685577\pi\) | |||||||
\(734\) | −1075.63 | −0.0540903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 5621.18 | 0.280948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9049.47 | 0.450460 | 0.225230 | − | 0.974306i | \(-0.427687\pi\) | ||||
0.225230 | + | 0.974306i | \(0.427687\pi\) | |||||||
\(740\) | −451.668 | −0.0224373 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26532.7 | 1.31273 | ||||||||
\(743\) | −10650.0 | −0.525855 | −0.262927 | − | 0.964816i | \(-0.584688\pi\) | ||||
−0.262927 | + | 0.964816i | \(0.584688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56166.8 | 2.76214 | ||||||||
\(746\) | 6148.39 | 0.301754 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1662.20 | −0.0812514 | ||||||||
\(749\) | −29960.1 | −1.46157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9340.20 | −0.453833 | −0.226917 | − | 0.973914i | \(-0.572864\pi\) | ||||
−0.226917 | + | 0.973914i | \(0.572864\pi\) | |||||||
\(752\) | 2314.29 | 0.112225 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17420.1 | 0.841384 | ||||||||
\(755\) | 64320.4 | 3.10048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12383.4 | −0.594562 | −0.297281 | − | 0.954790i | \(-0.596080\pi\) | ||||
−0.297281 | + | 0.954790i | \(0.596080\pi\) | |||||||
\(758\) | 18490.3 | 0.886013 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9985.28 | −0.476585 | ||||||||
\(761\) | 5906.69 | 0.281363 | 0.140682 | − | 0.990055i | \(-0.455071\pi\) | ||||
0.140682 | + | 0.990055i | \(0.455071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42311.2 | −2.00756 | ||||||||
\(764\) | 4075.73 | 0.193004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4058.91 | 0.191455 | ||||||||
\(767\) | −41974.0 | −1.97600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17056.5 | 0.799834 | 0.399917 | − | 0.916551i | \(-0.369039\pi\) | ||||
0.399917 | + | 0.916551i | \(0.369039\pi\) | |||||||
\(770\) | 27368.6 | 1.28090 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17211.7 | −0.802412 | ||||||||
\(773\) | −28498.6 | −1.32603 | −0.663017 | − | 0.748604i | \(-0.730724\pi\) | ||||
−0.663017 | + | 0.748604i | \(0.730724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 71560.7 | 3.31682 | ||||||||
\(776\) | 5974.89 | 0.276399 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14163.3 | 0.652674 | ||||||||
\(779\) | −10933.9 | −0.502884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12022.8 | 0.550843 | ||||||||
\(782\) | −701.074 | −0.0320593 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5664.53 | 0.258042 | ||||||||
\(785\) | 5586.59 | 0.254005 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30401.9 | 1.37701 | 0.688507 | − | 0.725230i | \(-0.258266\pi\) | ||||
0.688507 | + | 0.725230i | \(0.258266\pi\) | |||||||
\(788\) | 5757.43 | 0.260279 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25903.4 | −1.16659 | ||||||||
\(791\) | 54106.2 | 2.43210 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44457.4 | 1.99083 | ||||||||
\(794\) | 7948.22 | 0.355254 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21051.7 | 0.937385 | ||||||||
\(797\) | −3453.59 | −0.153491 | −0.0767456 | − | 0.997051i | \(-0.524453\pi\) | ||||
−0.0767456 | + | 0.997051i | \(0.524453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2204.47 | −0.0976077 | ||||||||
\(800\) | 7563.95 | 0.334283 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2456.64 | −0.108163 | ||||||||
\(803\) | 10640.3 | 0.467608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11543.4 | 0.505404 | ||||||||
\(806\) | 42319.9 | 1.84945 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9344.01 | 0.406833 | ||||||||
\(809\) | 31655.0 | 1.37569 | 0.687844 | − | 0.725859i | \(-0.258557\pi\) | ||||
0.687844 | + | 0.725859i | \(0.258557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2071.19 | −0.0896786 | −0.0448393 | − | 0.998994i | \(-0.514278\pi\) | ||||
−0.0448393 | + | 0.998994i | \(0.514278\pi\) | |||||||
\(812\) | −13160.4 | −0.568768 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 323.913 | 0.0139473 | ||||||||
\(815\) | −24278.8 | −1.04350 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20898.8 | −0.894929 | ||||||||
\(818\) | −9119.74 | −0.389809 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12662.5 | 0.539261 | ||||||||
\(821\) | 3082.16 | 0.131021 | 0.0655105 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655105 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16572.0 | −0.701901 | −0.350951 | − | 0.936394i | \(-0.614142\pi\) | ||||
−0.350951 | + | 0.936394i | \(0.614142\pi\) | |||||||
\(824\) | 4867.01 | 0.205765 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31710.2 | 1.33576 | ||||||||
\(827\) | 5374.02 | 0.225965 | 0.112983 | − | 0.993597i | \(-0.463960\pi\) | ||||
0.112983 | + | 0.993597i | \(0.463960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19312.7 | −0.809117 | −0.404559 | − | 0.914512i | \(-0.632575\pi\) | ||||
−0.404559 | + | 0.914512i | \(0.632575\pi\) | |||||||
\(830\) | 26433.9 | 1.10546 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4473.20 | 0.186395 | ||||||||
\(833\) | −5395.73 | −0.224431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28701.8 | −1.18954 | ||||||||
\(836\) | 7160.93 | 0.296251 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32729.2 | 1.34918 | ||||||||
\(839\) | 8072.94 | 0.332192 | 0.166096 | − | 0.986110i | \(-0.446884\pi\) | ||||
0.166096 | + | 0.986110i | \(0.446884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8859.21 | −0.363246 | ||||||||
\(842\) | 16935.0 | 0.693134 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1414.77 | 0.0576997 | ||||||||
\(845\) | −51101.2 | −2.08039 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15512.9 | 0.629316 | ||||||||
\(848\) | −8039.80 | −0.325575 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7205.02 | −0.290741 | ||||||||
\(851\) | 136.618 | 0.00550319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3676.62 | −0.147579 | −0.0737896 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737896 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(854\) | −33586.3 | −1.34578 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9078.34 | 0.362490 | ||||||||
\(857\) | 33806.9 | 1.34752 | 0.673758 | − | 0.738952i | \(-0.264679\pi\) | ||||
0.673758 | + | 0.738952i | \(0.264679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16752.0 | −0.665391 | −0.332696 | − | 0.943034i | \(-0.607958\pi\) | ||||
−0.332696 | + | 0.943034i | \(0.607958\pi\) | |||||||
\(860\) | 24202.9 | 0.959665 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24881.0 | 0.983122 | ||||||||
\(863\) | −26052.3 | −1.02761 | −0.513806 | − | 0.857906i | \(-0.671765\pi\) | ||||
−0.513806 | + | 0.857906i | \(0.671765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2619.11 | −0.102951 | ||||||||
\(866\) | 8158.46 | 0.320134 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31971.5 | −1.25021 | ||||||||
\(869\) | 18576.6 | 0.725165 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14409.5 | 0.560560 | ||||||||
\(872\) | 12820.9 | 0.497902 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3020.30 | 0.116891 | ||||||||
\(875\) | 55896.8 | 2.15961 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7214.34 | −0.277778 | −0.138889 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138889 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(878\) | 6972.45 | 0.268005 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8293.07 | −0.317681 | ||||||||
\(881\) | −30172.3 | −1.15384 | −0.576919 | − | 0.816801i | \(-0.695745\pi\) | ||||
−0.576919 | + | 0.816801i | \(0.695745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37498.4 | 1.42913 | 0.714564 | − | 0.699570i | \(-0.246625\pi\) | ||||
0.714564 | + | 0.699570i | \(0.246625\pi\) | |||||||
\(884\) | −4260.93 | −0.162116 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22640.6 | 0.858494 | ||||||||
\(887\) | 17991.8 | 0.681065 | 0.340533 | − | 0.940233i | \(-0.389393\pi\) | ||||
0.340533 | + | 0.940233i | \(0.389393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34924.9 | −1.31760 | ||||||||
\(890\) | −36076.8 | −1.35876 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21345.2 | −0.801223 | ||||||||
\(893\) | 9497.08 | 0.355888 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 57865.4 | 2.16115 | ||||||||
\(896\) | −3379.38 | −0.126001 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33709.3 | −1.25266 | ||||||||
\(899\) | 37727.6 | 1.39965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7658.28 | 0.283168 | ||||||||
\(902\) | −9080.89 | −0.335211 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16394.9 | −0.603194 | ||||||||
\(905\) | −74269.5 | −2.72796 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44123.2 | 1.61531 | 0.807655 | − | 0.589655i | \(-0.200736\pi\) | ||||
0.807655 | + | 0.589655i | \(0.200736\pi\) | |||||||
\(908\) | 8853.19 | 0.323572 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 70157.4 | 2.55571 | ||||||||
\(911\) | −10096.6 | −0.367196 | −0.183598 | − | 0.983001i | \(-0.558774\pi\) | ||||
−0.183598 | + | 0.983001i | \(0.558774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18957.0 | −0.687169 | ||||||||
\(914\) | −10659.1 | −0.385744 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20564.4 | −0.741774 | ||||||||
\(917\) | −9335.29 | −0.336181 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40900.3 | 1.46809 | 0.734045 | − | 0.679100i | \(-0.237630\pi\) | ||||
0.734045 | + | 0.679100i | \(0.237630\pi\) | |||||||
\(920\) | −3497.81 | −0.125347 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17224.6 | 0.615252 | ||||||||
\(923\) | 30819.5 | 1.09907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1404.04 | 0.0499077 | ||||||||
\(926\) | −23107.9 | −0.820056 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3987.79 | 0.141062 | ||||||||
\(929\) | 22417.0 | 0.791688 | 0.395844 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395844 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23245.4 | 0.818298 | ||||||||
\(932\) | 26329.3 | 0.925372 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12851.1 | 0.450214 | ||||||||
\(935\) | 7899.53 | 0.276302 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3106.56 | 0.108310 | 0.0541552 | − | 0.998533i | \(-0.482753\pi\) | ||||
0.0541552 | + | 0.998533i | \(0.482753\pi\) | |||||||
\(938\) | −10886.0 | −0.378933 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10998.6 | −0.381632 | ||||||||
\(941\) | −19428.6 | −0.673066 | −0.336533 | − | 0.941672i | \(-0.609254\pi\) | ||||
−0.336533 | + | 0.941672i | \(0.609254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3830.09 | −0.132264 | ||||||||
\(944\) | −9608.63 | −0.331286 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17357.1 | −0.596540 | ||||||||
\(947\) | −26080.2 | −0.894924 | −0.447462 | − | 0.894303i | \(-0.647672\pi\) | ||||
−0.447462 | + | 0.894303i | \(0.647672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27275.8 | 0.932992 | ||||||||
\(950\) | 31040.0 | 1.06007 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3219.01 | 0.109589 | ||||||||
\(953\) | −12821.6 | −0.435815 | −0.217907 | − | 0.975969i | \(-0.569923\pi\) | ||||
−0.217907 | + | 0.975969i | \(0.569923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19369.7 | −0.656325 | ||||||||
\(956\) | 24823.8 | 0.839812 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17332.2 | 0.584528 | ||||||||
\(959\) | −83739.8 | −2.81971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61863.1 | 2.07657 | ||||||||
\(962\) | 830.328 | 0.0278283 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25453.9 | −0.850432 | ||||||||
\(965\) | 81797.8 | 2.72867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4778.68 | −0.158916 | −0.0794582 | − | 0.996838i | \(-0.525319\pi\) | ||||
−0.0794582 | + | 0.996838i | \(0.525319\pi\) | |||||||
\(968\) | −4700.64 | −0.156079 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28395.4 | −0.939918 | ||||||||
\(971\) | −7439.58 | −0.245878 | −0.122939 | − | 0.992414i | \(-0.539232\pi\) | ||||
−0.122939 | + | 0.992414i | \(0.539232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13413.4 | −0.441945 | ||||||||
\(974\) | −37127.2 | −1.22139 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10177.1 | 0.333773 | ||||||||
\(977\) | 9975.97 | 0.326673 | 0.163336 | − | 0.986570i | \(-0.447774\pi\) | ||||
0.163336 | + | 0.986570i | \(0.447774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25872.4 | 0.844624 | ||||||||
\(980\) | −26920.4 | −0.877492 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23594.5 | −0.766732 | ||||||||
\(983\) | 21419.6 | 0.694995 | 0.347497 | − | 0.937681i | \(-0.387032\pi\) | ||||
0.347497 | + | 0.937681i | \(0.387032\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27361.9 | −0.885100 | ||||||||
\(986\) | −3798.56 | −0.122688 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18356.5 | 0.591093 | ||||||||
\(989\) | −7320.78 | −0.235376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43927.4 | −1.40807 | −0.704037 | − | 0.710164i | \(-0.748621\pi\) | ||||
−0.704037 | + | 0.710164i | \(0.748621\pi\) | |||||||
\(992\) | 9687.82 | 0.310069 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23283.3 | −0.742958 | ||||||||
\(995\) | −100047. | −3.18765 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39862.3 | −1.26625 | −0.633125 | − | 0.774049i | \(-0.718228\pi\) | ||||
−0.633125 | + | 0.774049i | \(0.718228\pi\) | |||||||
\(998\) | −6906.58 | −0.219062 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 414.4.a.n.1.1 | yes | 4 | |
3.2 | odd | 2 | 414.4.a.m.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.4.a.m.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
414.4.a.n.1.1 | yes | 4 | 1.1 | even | 1 | trivial |