Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,4,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(122.133953712\) |
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: | \( x^{4} - 68x^{2} - 111x + 342 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.57209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-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 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.4229 | −1.91266 | −0.956328 | − | 0.292294i | \(-0.905581\pi\) | ||||
−0.956328 | + | 0.292294i | \(0.905581\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 16.6298 | 0.455826 | 0.227913 | − | 0.973682i | \(-0.426810\pi\) | ||||
0.227913 | + | 0.973682i | \(0.426810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −79.9132 | −1.70492 | −0.852459 | − | 0.522795i | \(-0.824889\pi\) | ||||
−0.852459 | + | 0.522795i | \(0.824889\pi\) | |||||||
\(14\) | −70.8458 | −1.35245 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 46.8219 | 0.667999 | 0.333999 | − | 0.942573i | \(-0.391602\pi\) | ||||
0.333999 | + | 0.942573i | \(0.391602\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −110.653 | −1.33608 | −0.668042 | − | 0.744123i | \(-0.732868\pi\) | ||||
−0.668042 | + | 0.744123i | \(0.732868\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 33.2597 | 0.322318 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −159.826 | −1.20556 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −141.692 | −0.956328 | ||||||||
\(29\) | 0.836422 | 0.00535585 | 0.00267793 | − | 0.999996i | \(-0.499148\pi\) | ||||
0.00267793 | + | 0.999996i | \(0.499148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −119.836 | −0.694295 | −0.347147 | − | 0.937811i | \(-0.612850\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612850\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 93.6438 | 0.472346 | ||||||||
\(35\) | −177.114 | −0.855366 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 368.201 | 1.63600 | 0.817998 | − | 0.575221i | \(-0.195084\pi\) | ||||
0.817998 | + | 0.575221i | \(0.195084\pi\) | |||||||
\(38\) | −221.307 | −0.944755 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | 95.7927 | 0.364886 | 0.182443 | − | 0.983216i | \(-0.441600\pi\) | ||||
0.182443 | + | 0.983216i | \(0.441600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 331.961 | 1.17729 | 0.588647 | − | 0.808390i | \(-0.299661\pi\) | ||||
0.588647 | + | 0.808390i | \(0.299661\pi\) | |||||||
\(44\) | 66.5193 | 0.227913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 535.037 | 1.66049 | 0.830246 | − | 0.557397i | \(-0.188200\pi\) | ||||
0.830246 | + | 0.557397i | \(0.188200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 911.782 | 2.65826 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −319.653 | −0.852459 | ||||||||
\(53\) | −409.345 | −1.06090 | −0.530452 | − | 0.847715i | \(-0.677978\pi\) | ||||
−0.530452 | + | 0.847715i | \(0.677978\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.1492 | 0.203852 | ||||||||
\(56\) | −283.383 | −0.676226 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.67284 | 0.00378716 | ||||||||
\(59\) | 352.950 | 0.778817 | 0.389408 | − | 0.921065i | \(-0.372679\pi\) | ||||
0.389408 | + | 0.921065i | \(0.372679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −507.223 | −1.06464 | −0.532322 | − | 0.846542i | \(-0.678680\pi\) | ||||
−0.532322 | + | 0.846542i | \(0.678680\pi\) | |||||||
\(62\) | −239.672 | −0.490941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −399.566 | −0.762462 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −820.056 | −1.49531 | −0.747655 | − | 0.664087i | \(-0.768820\pi\) | ||||
−0.747655 | + | 0.664087i | \(0.768820\pi\) | |||||||
\(68\) | 187.288 | 0.333999 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −354.229 | −0.604835 | ||||||||
\(71\) | 733.770 | 1.22651 | 0.613257 | − | 0.789884i | \(-0.289859\pi\) | ||||
0.613257 | + | 0.789884i | \(0.289859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −91.4599 | −0.146638 | −0.0733190 | − | 0.997309i | \(-0.523359\pi\) | ||||
−0.0733190 | + | 0.997309i | \(0.523359\pi\) | |||||||
\(74\) | 736.402 | 1.15682 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −442.613 | −0.668042 | ||||||||
\(77\) | −589.077 | −0.871838 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 329.381 | 0.469092 | 0.234546 | − | 0.972105i | \(-0.424640\pi\) | ||||
0.234546 | + | 0.972105i | \(0.424640\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 191.585 | 0.258013 | ||||||||
\(83\) | 753.834 | 0.996916 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 234.110 | 0.298738 | ||||||||
\(86\) | 663.922 | 0.832472 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 133.039 | 0.161159 | ||||||||
\(89\) | 1050.14 | 1.25073 | 0.625365 | − | 0.780332i | \(-0.284950\pi\) | ||||
0.625365 | + | 0.780332i | \(0.284950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2830.76 | 3.26092 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1070.07 | 1.17415 | ||||||||
\(95\) | −553.267 | −0.597515 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −271.928 | −0.284641 | −0.142320 | − | 0.989821i | \(-0.545456\pi\) | ||||
−0.142320 | + | 0.989821i | \(0.545456\pi\) | |||||||
\(98\) | 1823.56 | 1.87967 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −1658.68 | −1.63410 | −0.817052 | − | 0.576563i | \(-0.804393\pi\) | ||||
−0.817052 | + | 0.576563i | \(0.804393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1735.52 | 1.66025 | 0.830123 | − | 0.557580i | \(-0.188270\pi\) | ||||
0.830123 | + | 0.557580i | \(0.188270\pi\) | |||||||
\(104\) | −639.305 | −0.602779 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −818.691 | −0.750172 | ||||||||
\(107\) | 1629.88 | 1.47258 | 0.736292 | − | 0.676664i | \(-0.236575\pi\) | ||||
0.736292 | + | 0.676664i | \(0.236575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −432.151 | −0.379748 | −0.189874 | − | 0.981808i | \(-0.560808\pi\) | ||||
−0.189874 | + | 0.981808i | \(0.560808\pi\) | |||||||
\(110\) | 166.298 | 0.144145 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −566.766 | −0.478164 | ||||||||
\(113\) | 240.115 | 0.199895 | 0.0999476 | − | 0.994993i | \(-0.468132\pi\) | ||||
0.0999476 | + | 0.994993i | \(0.468132\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 3.34569 | 0.00267793 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 705.900 | 0.550707 | ||||||||
\(119\) | −1658.57 | −1.27765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1054.45 | −0.792223 | ||||||||
\(122\) | −1014.45 | −0.752817 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −479.343 | −0.347147 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −210.993 | −0.147422 | −0.0737110 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737110 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −799.132 | −0.539142 | ||||||||
\(131\) | 746.178 | 0.497663 | 0.248832 | − | 0.968547i | \(-0.419953\pi\) | ||||
0.248832 | + | 0.968547i | \(0.419953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3919.66 | 2.55547 | ||||||||
\(134\) | −1640.11 | −1.05734 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 374.575 | 0.236173 | ||||||||
\(137\) | 2420.07 | 1.50920 | 0.754601 | − | 0.656184i | \(-0.227830\pi\) | ||||
0.754601 | + | 0.656184i | \(0.227830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 924.030 | 0.563850 | 0.281925 | − | 0.959436i | \(-0.409027\pi\) | ||||
0.281925 | + | 0.959436i | \(0.409027\pi\) | |||||||
\(140\) | −708.458 | −0.427683 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1467.54 | 0.867276 | ||||||||
\(143\) | −1328.94 | −0.777145 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.18211 | 0.00239521 | ||||||||
\(146\) | −182.920 | −0.103689 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1472.80 | 0.817998 | ||||||||
\(149\) | −430.614 | −0.236760 | −0.118380 | − | 0.992968i | \(-0.537770\pi\) | ||||
−0.118380 | + | 0.992968i | \(0.537770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −25.4118 | −0.0136953 | −0.00684763 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684763 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(152\) | −885.226 | −0.472377 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1178.15 | −0.616483 | ||||||||
\(155\) | −599.179 | −0.310498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1580.29 | −0.803317 | −0.401658 | − | 0.915790i | \(-0.631566\pi\) | ||||
−0.401658 | + | 0.915790i | \(0.631566\pi\) | |||||||
\(158\) | 658.762 | 0.331698 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | −814.727 | −0.398817 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 458.739 | 0.220437 | 0.110218 | − | 0.993907i | \(-0.464845\pi\) | ||||
0.110218 | + | 0.993907i | \(0.464845\pi\) | |||||||
\(164\) | 383.171 | 0.182443 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1507.67 | 0.704926 | ||||||||
\(167\) | 561.275 | 0.260076 | 0.130038 | − | 0.991509i | \(-0.458490\pi\) | ||||
0.130038 | + | 0.991509i | \(0.458490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4189.11 | 1.90674 | ||||||||
\(170\) | 468.219 | 0.211240 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1327.84 | 0.588647 | ||||||||
\(173\) | −1573.95 | −0.691705 | −0.345852 | − | 0.938289i | \(-0.612410\pi\) | ||||
−0.345852 | + | 0.938289i | \(0.612410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −885.572 | −0.382531 | ||||||||
\(176\) | 266.077 | 0.113956 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2100.29 | 0.884400 | ||||||||
\(179\) | −2215.59 | −0.925145 | −0.462572 | − | 0.886581i | \(-0.653073\pi\) | ||||
−0.462572 | + | 0.886581i | \(0.653073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 873.497 | 0.358710 | 0.179355 | − | 0.983784i | \(-0.442599\pi\) | ||||
0.179355 | + | 0.983784i | \(0.442599\pi\) | |||||||
\(182\) | 5661.51 | 2.30582 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 1841.00 | 0.731640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 778.641 | 0.304491 | ||||||||
\(188\) | 2140.15 | 0.830246 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1106.53 | −0.422507 | ||||||||
\(191\) | 2497.74 | 0.946230 | 0.473115 | − | 0.881001i | \(-0.343130\pi\) | ||||
0.473115 | + | 0.881001i | \(0.343130\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 909.155 | 0.339080 | 0.169540 | − | 0.985523i | \(-0.445772\pi\) | ||||
0.169540 | + | 0.985523i | \(0.445772\pi\) | |||||||
\(194\) | −543.857 | −0.201271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3647.13 | 1.32913 | ||||||||
\(197\) | −608.627 | −0.220116 | −0.110058 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110058 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2304.98 | −0.821083 | −0.410542 | − | 0.911842i | \(-0.634660\pi\) | ||||
−0.410542 | + | 0.911842i | \(0.634660\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3317.36 | −1.15549 | ||||||||
\(203\) | −29.6285 | −0.0102439 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 478.963 | 0.163182 | ||||||||
\(206\) | 3471.03 | 1.17397 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1278.61 | −0.426229 | ||||||||
\(209\) | −1840.15 | −0.609022 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4373.37 | −1.42690 | −0.713448 | − | 0.700708i | \(-0.752868\pi\) | ||||
−0.713448 | + | 0.700708i | \(0.752868\pi\) | |||||||
\(212\) | −1637.38 | −0.530452 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3259.76 | 1.04127 | ||||||||
\(215\) | 1659.81 | 0.526502 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4244.93 | 1.32795 | ||||||||
\(218\) | −864.303 | −0.268523 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 332.597 | 0.101926 | ||||||||
\(221\) | −3741.69 | −1.13888 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5439.50 | 1.63343 | 0.816717 | − | 0.577038i | \(-0.195792\pi\) | ||||
0.816717 | + | 0.577038i | \(0.195792\pi\) | |||||||
\(224\) | −1133.53 | −0.338113 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 480.231 | 0.141347 | ||||||||
\(227\) | −216.498 | −0.0633017 | −0.0316508 | − | 0.999499i | \(-0.510076\pi\) | ||||
−0.0316508 | + | 0.999499i | \(0.510076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −924.664 | −0.266828 | −0.133414 | − | 0.991060i | \(-0.542594\pi\) | ||||
−0.133414 | + | 0.991060i | \(0.542594\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.69138 | 0.00189358 | ||||||||
\(233\) | 2369.69 | 0.666280 | 0.333140 | − | 0.942877i | \(-0.391892\pi\) | ||||
0.333140 | + | 0.942877i | \(0.391892\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2675.18 | 0.742595 | ||||||||
\(236\) | 1411.80 | 0.389408 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3317.14 | −0.903437 | ||||||||
\(239\) | 2769.60 | 0.749583 | 0.374791 | − | 0.927109i | \(-0.377714\pi\) | ||||
0.374791 | + | 0.927109i | \(0.377714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5334.10 | −1.42572 | −0.712862 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712862 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(242\) | −2108.90 | −0.560186 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2028.89 | −0.532322 | ||||||||
\(245\) | 4558.91 | 1.18881 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8842.66 | 2.27791 | ||||||||
\(248\) | −958.686 | −0.245470 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −4677.13 | −1.17617 | −0.588084 | − | 0.808800i | \(-0.700118\pi\) | ||||
−0.588084 | + | 0.808800i | \(0.700118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 382.486 | 0.0950463 | ||||||||
\(254\) | −421.986 | −0.104243 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2602.99 | 0.631789 | 0.315895 | − | 0.948794i | \(-0.397695\pi\) | ||||
0.315895 | + | 0.948794i | \(0.397695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13042.7 | −3.12910 | ||||||||
\(260\) | −1598.26 | −0.381231 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1492.36 | 0.351901 | ||||||||
\(263\) | 3411.30 | 0.799809 | 0.399904 | − | 0.916557i | \(-0.369043\pi\) | ||||
0.399904 | + | 0.916557i | \(0.369043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2046.73 | −0.474451 | ||||||||
\(266\) | 7839.32 | 1.80699 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3280.22 | −0.747655 | ||||||||
\(269\) | −4366.56 | −0.989718 | −0.494859 | − | 0.868973i | \(-0.664780\pi\) | ||||
−0.494859 | + | 0.868973i | \(0.664780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5682.45 | 1.27374 | 0.636872 | − | 0.770970i | \(-0.280228\pi\) | ||||
0.636872 | + | 0.770970i | \(0.280228\pi\) | |||||||
\(272\) | 749.150 | 0.167000 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4840.14 | 1.06717 | ||||||||
\(275\) | 415.746 | 0.0911652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1884.62 | −0.408794 | −0.204397 | − | 0.978888i | \(-0.565523\pi\) | ||||
−0.204397 | + | 0.978888i | \(0.565523\pi\) | |||||||
\(278\) | 1848.06 | 0.398702 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1416.92 | −0.302418 | ||||||||
\(281\) | 2706.42 | 0.574561 | 0.287281 | − | 0.957846i | \(-0.407249\pi\) | ||||
0.287281 | + | 0.957846i | \(0.407249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5963.64 | −1.25266 | −0.626328 | − | 0.779560i | \(-0.715443\pi\) | ||||
−0.626328 | + | 0.779560i | \(0.715443\pi\) | |||||||
\(284\) | 2935.08 | 0.613257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2657.89 | −0.549525 | ||||||||
\(287\) | −3393.26 | −0.697901 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2720.71 | −0.553778 | ||||||||
\(290\) | 8.36422 | 0.00169367 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −365.840 | −0.0733190 | ||||||||
\(293\) | 4735.85 | 0.944272 | 0.472136 | − | 0.881526i | \(-0.343483\pi\) | ||||
0.472136 | + | 0.881526i | \(0.343483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1764.75 | 0.348297 | ||||||||
\(296\) | 2945.61 | 0.578412 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −861.227 | −0.167415 | ||||||||
\(299\) | −1838.00 | −0.355500 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11759.0 | −2.25176 | ||||||||
\(302\) | −50.8236 | −0.00968401 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1770.45 | −0.334021 | ||||||||
\(305\) | −2536.12 | −0.476123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −769.241 | −0.143006 | −0.0715031 | − | 0.997440i | \(-0.522780\pi\) | ||||
−0.0715031 | + | 0.997440i | \(0.522780\pi\) | |||||||
\(308\) | −2356.31 | −0.435919 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1198.36 | −0.219555 | ||||||||
\(311\) | 5592.71 | 1.01972 | 0.509861 | − | 0.860257i | \(-0.329697\pi\) | ||||
0.509861 | + | 0.860257i | \(0.329697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9777.19 | 1.76562 | 0.882811 | − | 0.469729i | \(-0.155648\pi\) | ||||
0.882811 | + | 0.469729i | \(0.155648\pi\) | |||||||
\(314\) | −3160.58 | −0.568031 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1317.52 | 0.234546 | ||||||||
\(317\) | −1868.51 | −0.331060 | −0.165530 | − | 0.986205i | \(-0.552934\pi\) | ||||
−0.165530 | + | 0.986205i | \(0.552934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.9096 | 0.00244134 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1629.45 | −0.282006 | ||||||||
\(323\) | −5181.00 | −0.892503 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1997.83 | −0.340983 | ||||||||
\(326\) | 917.477 | 0.155872 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 766.342 | 0.129007 | ||||||||
\(329\) | −18952.6 | −3.17595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6966.91 | 1.15691 | 0.578454 | − | 0.815715i | \(-0.303656\pi\) | ||||
0.578454 | + | 0.815715i | \(0.303656\pi\) | |||||||
\(332\) | 3015.34 | 0.498458 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1122.55 | 0.183902 | ||||||||
\(335\) | −4100.28 | −0.668723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5487 | −0.00283661 | −0.00141830 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141830 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(338\) | 8378.23 | 1.34827 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 936.438 | 0.149369 | ||||||||
\(341\) | −1992.85 | −0.316477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20147.9 | −3.17167 | ||||||||
\(344\) | 2655.69 | 0.416236 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3147.89 | −0.489109 | ||||||||
\(347\) | 9859.30 | 1.52529 | 0.762644 | − | 0.646818i | \(-0.223901\pi\) | ||||
0.762644 | + | 0.646818i | \(0.223901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7200.25 | 1.10436 | 0.552178 | − | 0.833726i | \(-0.313797\pi\) | ||||
0.552178 | + | 0.833726i | \(0.313797\pi\) | |||||||
\(350\) | −1771.14 | −0.270491 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 532.155 | 0.0805794 | ||||||||
\(353\) | 6054.58 | 0.912897 | 0.456449 | − | 0.889750i | \(-0.349121\pi\) | ||||
0.456449 | + | 0.889750i | \(0.349121\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3668.85 | 0.548513 | ||||||||
\(356\) | 4200.57 | 0.625365 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4431.18 | −0.654176 | ||||||||
\(359\) | −2734.26 | −0.401974 | −0.200987 | − | 0.979594i | \(-0.564415\pi\) | ||||
−0.200987 | + | 0.979594i | \(0.564415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5385.16 | 0.785123 | ||||||||
\(362\) | 1746.99 | 0.253646 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11323.0 | 1.63046 | ||||||||
\(365\) | −457.300 | −0.0655785 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2465.50 | −0.350676 | −0.175338 | − | 0.984508i | \(-0.556102\pi\) | ||||
−0.175338 | + | 0.984508i | \(0.556102\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3682.01 | 0.517347 | ||||||||
\(371\) | 14500.2 | 2.02915 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5704.45 | 0.791863 | 0.395932 | − | 0.918280i | \(-0.370422\pi\) | ||||
0.395932 | + | 0.918280i | \(0.370422\pi\) | |||||||
\(374\) | 1557.28 | 0.215308 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4280.29 | 0.587073 | ||||||||
\(377\) | −66.8411 | −0.00913128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10231.9 | 1.38675 | 0.693376 | − | 0.720576i | \(-0.256122\pi\) | ||||
0.693376 | + | 0.720576i | \(0.256122\pi\) | |||||||
\(380\) | −2213.07 | −0.298758 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4995.47 | 0.669086 | ||||||||
\(383\) | −6321.34 | −0.843356 | −0.421678 | − | 0.906746i | \(-0.638559\pi\) | ||||
−0.421678 | + | 0.906746i | \(0.638559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2945.38 | −0.389898 | ||||||||
\(386\) | 1818.31 | 0.239766 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1087.71 | −0.142320 | ||||||||
\(389\) | 925.594 | 0.120641 | 0.0603207 | − | 0.998179i | \(-0.480788\pi\) | ||||
0.0603207 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1076.90 | 0.139287 | ||||||||
\(392\) | 7294.25 | 0.939835 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1217.25 | −0.155646 | ||||||||
\(395\) | 1646.91 | 0.209784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2706.75 | −0.342187 | −0.171093 | − | 0.985255i | \(-0.554730\pi\) | ||||
−0.171093 | + | 0.985255i | \(0.554730\pi\) | |||||||
\(398\) | −4609.96 | −0.580594 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 14095.3 | 1.75532 | 0.877661 | − | 0.479281i | \(-0.159103\pi\) | ||||
0.877661 | + | 0.479281i | \(0.159103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9576.45 | 1.18372 | ||||||||
\(404\) | −6634.71 | −0.817052 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −59.2570 | −0.00724353 | ||||||||
\(407\) | 6123.12 | 0.745729 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10846.0 | −1.31125 | −0.655625 | − | 0.755087i | \(-0.727595\pi\) | ||||
−0.655625 | + | 0.755087i | \(0.727595\pi\) | |||||||
\(410\) | 957.927 | 0.115387 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6942.06 | 0.830123 | ||||||||
\(413\) | −12502.5 | −1.48961 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3769.17 | 0.445834 | ||||||||
\(416\) | −2557.22 | −0.301390 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3680.29 | −0.430644 | ||||||||
\(419\) | 5626.55 | 0.656026 | 0.328013 | − | 0.944673i | \(-0.393621\pi\) | ||||
0.328013 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7109.09 | −0.822983 | −0.411491 | − | 0.911414i | \(-0.634992\pi\) | ||||
−0.411491 | + | 0.911414i | \(0.634992\pi\) | |||||||
\(422\) | −8746.74 | −1.00897 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3274.76 | −0.375086 | ||||||||
\(425\) | 1170.55 | 0.133600 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17967.3 | 2.03630 | ||||||||
\(428\) | 6519.52 | 0.736292 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3319.61 | 0.372293 | ||||||||
\(431\) | −4464.14 | −0.498909 | −0.249455 | − | 0.968387i | \(-0.580251\pi\) | ||||
−0.249455 | + | 0.968387i | \(0.580251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11009.4 | 1.22189 | 0.610947 | − | 0.791672i | \(-0.290789\pi\) | ||||
0.610947 | + | 0.791672i | \(0.290789\pi\) | |||||||
\(434\) | 8489.86 | 0.939001 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1728.61 | −0.189874 | ||||||||
\(437\) | −2545.03 | −0.278593 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3052.70 | −0.331885 | −0.165943 | − | 0.986135i | \(-0.553067\pi\) | ||||
−0.165943 | + | 0.986135i | \(0.553067\pi\) | |||||||
\(440\) | 665.193 | 0.0720724 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7483.37 | −0.805312 | ||||||||
\(443\) | 4465.82 | 0.478956 | 0.239478 | − | 0.970902i | \(-0.423024\pi\) | ||||
0.239478 | + | 0.970902i | \(0.423024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5250.72 | 0.559343 | ||||||||
\(446\) | 10879.0 | 1.15501 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2267.07 | −0.239082 | ||||||||
\(449\) | −9040.14 | −0.950179 | −0.475090 | − | 0.879937i | \(-0.657584\pi\) | ||||
−0.475090 | + | 0.879937i | \(0.657584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1593.02 | 0.166324 | ||||||||
\(452\) | 960.462 | 0.0999476 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −432.996 | −0.0447610 | ||||||||
\(455\) | 14153.8 | 1.45833 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7756.88 | 0.793986 | 0.396993 | − | 0.917822i | \(-0.370054\pi\) | ||||
0.396993 | + | 0.917822i | \(0.370054\pi\) | |||||||
\(458\) | −1849.33 | −0.188676 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 460.000 | 0.0466252 | ||||||||
\(461\) | −7064.19 | −0.713692 | −0.356846 | − | 0.934163i | \(-0.616148\pi\) | ||||
−0.356846 | + | 0.934163i | \(0.616148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12599.7 | 1.26470 | 0.632350 | − | 0.774682i | \(-0.282090\pi\) | ||||
0.632350 | + | 0.774682i | \(0.282090\pi\) | |||||||
\(464\) | 13.3828 | 0.00133896 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4739.37 | 0.471131 | ||||||||
\(467\) | −14746.0 | −1.46117 | −0.730583 | − | 0.682824i | \(-0.760751\pi\) | ||||
−0.730583 | + | 0.682824i | \(0.760751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29048.8 | 2.86002 | ||||||||
\(470\) | 5350.37 | 0.525094 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2823.60 | 0.275353 | ||||||||
\(473\) | 5520.46 | 0.536641 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2766.33 | −0.267217 | ||||||||
\(476\) | −6634.27 | −0.638826 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5539.19 | 0.530035 | ||||||||
\(479\) | 17411.2 | 1.66084 | 0.830418 | − | 0.557141i | \(-0.188102\pi\) | ||||
0.830418 | + | 0.557141i | \(0.188102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29424.1 | −2.78924 | ||||||||
\(482\) | −10668.2 | −1.00814 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4217.79 | −0.396111 | ||||||||
\(485\) | −1359.64 | −0.127295 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1320.34 | 0.122855 | 0.0614276 | − | 0.998112i | \(-0.480435\pi\) | ||||
0.0614276 | + | 0.998112i | \(0.480435\pi\) | |||||||
\(488\) | −4057.78 | −0.376408 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9117.82 | 0.840614 | ||||||||
\(491\) | −17115.8 | −1.57317 | −0.786583 | − | 0.617485i | \(-0.788152\pi\) | ||||
−0.786583 | + | 0.617485i | \(0.788152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.1629 | 0.00357770 | ||||||||
\(494\) | 17685.3 | 1.61073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1917.37 | −0.173574 | ||||||||
\(497\) | −25992.3 | −2.34590 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17540.6 | 1.57360 | 0.786798 | − | 0.617210i | \(-0.211737\pi\) | ||||
0.786798 | + | 0.617210i | \(0.211737\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9354.27 | −0.831676 | ||||||||
\(503\) | 4934.98 | 0.437455 | 0.218727 | − | 0.975786i | \(-0.429809\pi\) | ||||
0.218727 | + | 0.975786i | \(0.429809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8293.39 | −0.730794 | ||||||||
\(506\) | 764.972 | 0.0672079 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −843.972 | −0.0737110 | ||||||||
\(509\) | −11927.3 | −1.03865 | −0.519323 | − | 0.854578i | \(-0.673816\pi\) | ||||
−0.519323 | + | 0.854578i | \(0.673816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3239.78 | 0.280468 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5205.97 | 0.446743 | ||||||||
\(515\) | 8677.58 | 0.742485 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8897.57 | 0.756895 | ||||||||
\(518\) | −26085.5 | −2.21261 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3196.53 | −0.269571 | ||||||||
\(521\) | 9592.76 | 0.806653 | 0.403327 | − | 0.915056i | \(-0.367854\pi\) | ||||
0.403327 | + | 0.915056i | \(0.367854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6525.20 | 0.545558 | 0.272779 | − | 0.962077i | \(-0.412057\pi\) | ||||
0.272779 | + | 0.962077i | \(0.412057\pi\) | |||||||
\(524\) | 2984.71 | 0.248832 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6822.60 | 0.565550 | ||||||||
\(527\) | −5610.94 | −0.463788 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −4093.45 | −0.335487 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15678.6 | 1.27774 | ||||||||
\(533\) | −7655.10 | −0.622100 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8149.40 | 0.658560 | ||||||||
\(536\) | −6560.45 | −0.528672 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8733.13 | −0.699836 | ||||||||
\(539\) | 15162.8 | 1.21170 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5634.05 | 0.447739 | 0.223870 | − | 0.974619i | \(-0.428131\pi\) | ||||
0.223870 | + | 0.974619i | \(0.428131\pi\) | |||||||
\(542\) | 11364.9 | 0.900673 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1498.30 | 0.118087 | ||||||||
\(545\) | −2160.76 | −0.169829 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6093.08 | 0.476273 | 0.238136 | − | 0.971232i | \(-0.423463\pi\) | ||||
0.238136 | + | 0.971232i | \(0.423463\pi\) | |||||||
\(548\) | 9680.29 | 0.754601 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 831.492 | 0.0644635 | ||||||||
\(551\) | −92.5529 | −0.00715587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11667.6 | −0.897212 | ||||||||
\(554\) | −3769.24 | −0.289061 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3696.12 | 0.281925 | ||||||||
\(557\) | −21461.9 | −1.63262 | −0.816311 | − | 0.577612i | \(-0.803985\pi\) | ||||
−0.816311 | + | 0.577612i | \(0.803985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26528.1 | −2.00719 | ||||||||
\(560\) | −2833.83 | −0.213842 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5412.85 | 0.406276 | ||||||||
\(563\) | 11038.5 | 0.826316 | 0.413158 | − | 0.910659i | \(-0.364426\pi\) | ||||
0.413158 | + | 0.910659i | \(0.364426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1200.58 | 0.0893959 | ||||||||
\(566\) | −11927.3 | −0.885761 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5870.16 | 0.433638 | ||||||||
\(569\) | 19210.3 | 1.41535 | 0.707677 | − | 0.706536i | \(-0.249743\pi\) | ||||
0.707677 | + | 0.706536i | \(0.249743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11967.0 | −0.877066 | −0.438533 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438533 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(572\) | −5315.77 | −0.388573 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6786.51 | −0.493490 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14982.3 | −1.08097 | −0.540487 | − | 0.841352i | \(-0.681760\pi\) | ||||
−0.540487 | + | 0.841352i | \(0.681760\pi\) | |||||||
\(578\) | −5441.42 | −0.391580 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.7284 | 0.00119760 | ||||||||
\(581\) | −26703.0 | −1.90676 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6807.35 | −0.483587 | ||||||||
\(584\) | −731.679 | −0.0518444 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9471.71 | 0.667701 | ||||||||
\(587\) | −24002.9 | −1.68774 | −0.843871 | − | 0.536547i | \(-0.819729\pi\) | ||||
−0.843871 | + | 0.536547i | \(0.819729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13260.2 | 0.927637 | ||||||||
\(590\) | 3529.50 | 0.246283 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5891.21 | 0.408999 | ||||||||
\(593\) | −5124.67 | −0.354882 | −0.177441 | − | 0.984131i | \(-0.556782\pi\) | ||||
−0.177441 | + | 0.984131i | \(0.556782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8292.84 | −0.571384 | ||||||||
\(596\) | −1722.45 | −0.118380 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3676.01 | −0.251376 | ||||||||
\(599\) | 23776.8 | 1.62186 | 0.810928 | − | 0.585146i | \(-0.198963\pi\) | ||||
0.810928 | + | 0.585146i | \(0.198963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25435.3 | −1.72633 | −0.863166 | − | 0.504920i | \(-0.831522\pi\) | ||||
−0.863166 | + | 0.504920i | \(0.831522\pi\) | |||||||
\(602\) | −23518.1 | −1.59223 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −101.647 | −0.00684763 | ||||||||
\(605\) | −5272.24 | −0.354293 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7445.94 | −0.497894 | −0.248947 | − | 0.968517i | \(-0.580084\pi\) | ||||
−0.248947 | + | 0.968517i | \(0.580084\pi\) | |||||||
\(608\) | −3540.91 | −0.236189 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5072.23 | −0.336670 | ||||||||
\(611\) | −42756.5 | −2.83100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12874.4 | −0.848275 | −0.424138 | − | 0.905598i | \(-0.639423\pi\) | ||||
−0.424138 | + | 0.905598i | \(0.639423\pi\) | |||||||
\(614\) | −1538.48 | −0.101121 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4712.62 | −0.308241 | ||||||||
\(617\) | 19247.2 | 1.25585 | 0.627927 | − | 0.778272i | \(-0.283904\pi\) | ||||
0.627927 | + | 0.778272i | \(0.283904\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14496.4 | −0.941293 | −0.470647 | − | 0.882322i | \(-0.655979\pi\) | ||||
−0.470647 | + | 0.882322i | \(0.655979\pi\) | |||||||
\(620\) | −2396.72 | −0.155249 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11185.4 | 0.721052 | ||||||||
\(623\) | −37199.1 | −2.39222 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 19554.4 | 1.24848 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6321.15 | −0.401658 | ||||||||
\(629\) | 17239.9 | 1.09284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18030.9 | −1.13756 | −0.568779 | − | 0.822490i | \(-0.692584\pi\) | ||||
−0.568779 | + | 0.822490i | \(0.692584\pi\) | |||||||
\(632\) | 2635.05 | 0.165849 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3737.03 | −0.234095 | ||||||||
\(635\) | −1054.96 | −0.0659291 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −72863.4 | −4.53211 | ||||||||
\(638\) | 27.8191 | 0.00172628 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −11776.4 | −0.725646 | −0.362823 | − | 0.931858i | \(-0.618187\pi\) | ||||
−0.362823 | + | 0.931858i | \(0.618187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20207.4 | 1.23935 | 0.619676 | − | 0.784858i | \(-0.287264\pi\) | ||||
0.619676 | + | 0.784858i | \(0.287264\pi\) | |||||||
\(644\) | −3258.91 | −0.199408 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10362.0 | −0.631095 | ||||||||
\(647\) | −21452.8 | −1.30355 | −0.651776 | − | 0.758412i | \(-0.725976\pi\) | ||||
−0.651776 | + | 0.758412i | \(0.725976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5869.50 | 0.355005 | ||||||||
\(650\) | −3995.66 | −0.241112 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1834.95 | 0.110218 | ||||||||
\(653\) | 15095.2 | 0.904624 | 0.452312 | − | 0.891860i | \(-0.350599\pi\) | ||||
0.452312 | + | 0.891860i | \(0.350599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3730.89 | 0.222562 | ||||||||
\(656\) | 1532.68 | 0.0912214 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −37905.1 | −2.24574 | ||||||||
\(659\) | −6964.68 | −0.411693 | −0.205846 | − | 0.978584i | \(-0.565995\pi\) | ||||
−0.205846 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17380.4 | −1.02272 | −0.511361 | − | 0.859366i | \(-0.670858\pi\) | ||||
−0.511361 | + | 0.859366i | \(0.670858\pi\) | |||||||
\(662\) | 13933.8 | 0.818057 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6030.67 | 0.352463 | ||||||||
\(665\) | 19598.3 | 1.14284 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.2377 | 0.00111677 | ||||||||
\(668\) | 2245.10 | 0.130038 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8200.56 | −0.472859 | ||||||||
\(671\) | −8435.04 | −0.485292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12383.2 | 0.709271 | 0.354635 | − | 0.935005i | \(-0.384605\pi\) | ||||
0.354635 | + | 0.935005i | \(0.384605\pi\) | |||||||
\(674\) | −35.0973 | −0.00200578 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16756.5 | 0.953371 | ||||||||
\(677\) | 8375.74 | 0.475489 | 0.237744 | − | 0.971328i | \(-0.423592\pi\) | ||||
0.237744 | + | 0.971328i | \(0.423592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9632.49 | 0.544420 | ||||||||
\(680\) | 1872.88 | 0.105620 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3985.70 | −0.223783 | ||||||||
\(683\) | 4434.66 | 0.248444 | 0.124222 | − | 0.992254i | \(-0.460356\pi\) | ||||
0.124222 | + | 0.992254i | \(0.460356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12100.4 | 0.674936 | ||||||||
\(686\) | −40295.8 | −2.24271 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5311.38 | 0.294323 | ||||||||
\(689\) | 32712.1 | 1.80875 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11032.8 | 0.607389 | 0.303694 | − | 0.952770i | \(-0.401780\pi\) | ||||
0.303694 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(692\) | −6295.79 | −0.345852 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19718.6 | 1.07854 | ||||||||
\(695\) | 4620.15 | 0.252162 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4485.20 | 0.243743 | ||||||||
\(698\) | 14400.5 | 0.780898 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3542.29 | −0.191266 | ||||||||
\(701\) | −3708.40 | −0.199806 | −0.0999032 | − | 0.994997i | \(-0.531853\pi\) | ||||
−0.0999032 | + | 0.994997i | \(0.531853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40742.6 | −2.18583 | ||||||||
\(704\) | 1064.31 | 0.0569782 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12109.2 | 0.645516 | ||||||||
\(707\) | 58755.2 | 3.12548 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6315.04 | −0.334508 | −0.167254 | − | 0.985914i | \(-0.553490\pi\) | ||||
−0.167254 | + | 0.985914i | \(0.553490\pi\) | |||||||
\(710\) | 7337.70 | 0.387858 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8401.15 | 0.442200 | ||||||||
\(713\) | −2756.22 | −0.144770 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6644.71 | −0.347550 | ||||||||
\(716\) | −8862.36 | −0.462572 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5468.52 | −0.284239 | ||||||||
\(719\) | −24736.9 | −1.28307 | −0.641536 | − | 0.767093i | \(-0.721703\pi\) | ||||
−0.641536 | + | 0.767093i | \(0.721703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −61477.0 | −3.17548 | ||||||||
\(722\) | 10770.3 | 0.555165 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3493.99 | 0.179355 | ||||||||
\(725\) | 20.9106 | 0.00107117 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33283.6 | 1.69797 | 0.848983 | − | 0.528420i | \(-0.177215\pi\) | ||||
0.848983 | + | 0.528420i | \(0.177215\pi\) | |||||||
\(728\) | 22646.0 | 1.15291 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −914.599 | −0.0463710 | ||||||||
\(731\) | 15543.1 | 0.786430 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33636.5 | −1.69494 | −0.847471 | − | 0.530841i | \(-0.821876\pi\) | ||||
−0.847471 | + | 0.530841i | \(0.821876\pi\) | |||||||
\(734\) | −4931.00 | −0.247965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −13637.4 | −0.681601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36575.5 | 1.82064 | 0.910319 | − | 0.413907i | \(-0.135836\pi\) | ||||
0.910319 | + | 0.413907i | \(0.135836\pi\) | |||||||
\(740\) | 7364.02 | 0.365820 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29000.4 | 1.43482 | ||||||||
\(743\) | 17704.7 | 0.874190 | 0.437095 | − | 0.899415i | \(-0.356007\pi\) | ||||
0.437095 | + | 0.899415i | \(0.356007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2153.07 | −0.105882 | ||||||||
\(746\) | 11408.9 | 0.559932 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3114.56 | 0.152246 | ||||||||
\(749\) | −57735.1 | −2.81655 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8858.37 | 0.430421 | 0.215211 | − | 0.976568i | \(-0.430956\pi\) | ||||
0.215211 | + | 0.976568i | \(0.430956\pi\) | |||||||
\(752\) | 8560.59 | 0.415123 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −133.682 | −0.00645679 | ||||||||
\(755\) | −127.059 | −0.00612470 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7899.26 | 0.379265 | 0.189633 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189633 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(758\) | 20463.9 | 0.980582 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4426.13 | −0.211254 | ||||||||
\(761\) | −23437.4 | −1.11643 | −0.558216 | − | 0.829696i | \(-0.688514\pi\) | ||||
−0.558216 | + | 0.829696i | \(0.688514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15308.1 | 0.726329 | ||||||||
\(764\) | 9990.95 | 0.473115 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12642.7 | −0.596343 | ||||||||
\(767\) | −28205.4 | −1.32782 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31447.7 | 1.47468 | 0.737342 | − | 0.675519i | \(-0.236081\pi\) | ||||
0.737342 | + | 0.675519i | \(0.236081\pi\) | |||||||
\(770\) | −5890.77 | −0.275699 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3636.62 | 0.169540 | ||||||||
\(773\) | −2397.42 | −0.111551 | −0.0557756 | − | 0.998443i | \(-0.517763\pi\) | ||||
−0.0557756 | + | 0.998443i | \(0.517763\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2995.89 | −0.138859 | ||||||||
\(776\) | −2175.43 | −0.100636 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1851.19 | 0.0853063 | ||||||||
\(779\) | −10599.8 | −0.487518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12202.5 | 0.559077 | ||||||||
\(782\) | 2153.81 | 0.0984911 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14588.5 | 0.664564 | ||||||||
\(785\) | −7901.44 | −0.359254 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19407.0 | −0.879014 | −0.439507 | − | 0.898239i | \(-0.644847\pi\) | ||||
−0.439507 | + | 0.898239i | \(0.644847\pi\) | |||||||
\(788\) | −2434.51 | −0.110058 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3293.81 | 0.148340 | ||||||||
\(791\) | −8505.58 | −0.382331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40533.8 | 1.81513 | ||||||||
\(794\) | −5413.51 | −0.241962 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9219.91 | −0.410542 | ||||||||
\(797\) | 28631.1 | 1.27248 | 0.636240 | − | 0.771491i | \(-0.280489\pi\) | ||||
0.636240 | + | 0.771491i | \(0.280489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25051.4 | 1.10921 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28190.6 | 1.24120 | ||||||||
\(803\) | −1520.96 | −0.0668414 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4073.63 | −0.178356 | ||||||||
\(806\) | 19152.9 | 0.837013 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13269.4 | −0.577743 | ||||||||
\(809\) | 9191.25 | 0.399440 | 0.199720 | − | 0.979853i | \(-0.435997\pi\) | ||||
0.199720 | + | 0.979853i | \(0.435997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −567.477 | −0.0245706 | −0.0122853 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122853 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(812\) | −118.514 | −0.00512195 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12246.2 | 0.527310 | ||||||||
\(815\) | 2293.69 | 0.0985823 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36732.6 | −1.57296 | ||||||||
\(818\) | −21692.0 | −0.927193 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1915.85 | 0.0815909 | ||||||||
\(821\) | 6057.35 | 0.257494 | 0.128747 | − | 0.991677i | \(-0.458904\pi\) | ||||
0.128747 | + | 0.991677i | \(0.458904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21327.0 | −0.903294 | −0.451647 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451647 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(824\) | 13884.1 | 0.586986 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25005.0 | −1.05331 | ||||||||
\(827\) | 27553.8 | 1.15857 | 0.579286 | − | 0.815124i | \(-0.303332\pi\) | ||||
0.579286 | + | 0.815124i | \(0.303332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11181.6 | 0.468461 | 0.234231 | − | 0.972181i | \(-0.424743\pi\) | ||||
0.234231 | + | 0.972181i | \(0.424743\pi\) | |||||||
\(830\) | 7538.34 | 0.315253 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5114.44 | −0.213115 | ||||||||
\(833\) | 42691.4 | 1.77571 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2806.37 | 0.116310 | ||||||||
\(836\) | −7360.59 | −0.304511 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11253.1 | 0.463881 | ||||||||
\(839\) | −9811.83 | −0.403745 | −0.201872 | − | 0.979412i | \(-0.564703\pi\) | ||||
−0.201872 | + | 0.979412i | \(0.564703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24388.3 | −0.999971 | ||||||||
\(842\) | −14218.2 | −0.581937 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17493.5 | −0.713448 | ||||||||
\(845\) | 20945.6 | 0.852721 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37351.6 | 1.51525 | ||||||||
\(848\) | −6549.53 | −0.265226 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2341.10 | 0.0944693 | ||||||||
\(851\) | 8468.62 | 0.341129 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24030.8 | −0.964594 | −0.482297 | − | 0.876008i | \(-0.660197\pi\) | ||||
−0.482297 | + | 0.876008i | \(0.660197\pi\) | |||||||
\(854\) | 35934.6 | 1.43988 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13039.0 | 0.520637 | ||||||||
\(857\) | 16934.8 | 0.675008 | 0.337504 | − | 0.941324i | \(-0.390417\pi\) | ||||
0.337504 | + | 0.941324i | \(0.390417\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31057.0 | −1.23359 | −0.616793 | − | 0.787125i | \(-0.711568\pi\) | ||||
−0.616793 | + | 0.787125i | \(0.711568\pi\) | |||||||
\(860\) | 6639.22 | 0.263251 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8928.27 | −0.352782 | ||||||||
\(863\) | 16157.8 | 0.637332 | 0.318666 | − | 0.947867i | \(-0.396765\pi\) | ||||
0.318666 | + | 0.947867i | \(0.396765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7869.73 | −0.309340 | ||||||||
\(866\) | 22018.9 | 0.864009 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16979.7 | 0.663974 | ||||||||
\(869\) | 5477.55 | 0.213824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65533.3 | 2.54938 | ||||||||
\(872\) | −3457.21 | −0.134261 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5090.05 | −0.196995 | ||||||||
\(875\) | −4427.86 | −0.171073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32473.9 | −1.25036 | −0.625180 | − | 0.780480i | \(-0.714975\pi\) | ||||
−0.625180 | + | 0.780480i | \(0.714975\pi\) | |||||||
\(878\) | −6105.41 | −0.234678 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1330.39 | 0.0509629 | ||||||||
\(881\) | 15703.2 | 0.600517 | 0.300258 | − | 0.953858i | \(-0.402927\pi\) | ||||
0.300258 | + | 0.953858i | \(0.402927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14330.4 | −0.546155 | −0.273078 | − | 0.961992i | \(-0.588042\pi\) | ||||
−0.273078 | + | 0.961992i | \(0.588042\pi\) | |||||||
\(884\) | −14966.7 | −0.569441 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8931.65 | 0.338673 | ||||||||
\(887\) | −23238.2 | −0.879664 | −0.439832 | − | 0.898080i | \(-0.644962\pi\) | ||||
−0.439832 | + | 0.898080i | \(0.644962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7473.98 | 0.281968 | ||||||||
\(890\) | 10501.4 | 0.395515 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21758.0 | 0.816717 | ||||||||
\(893\) | −59203.6 | −2.21856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11077.9 | −0.413737 | ||||||||
\(896\) | −4534.13 | −0.169057 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18080.3 | −0.671878 | ||||||||
\(899\) | −100.233 | −0.00371854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19166.3 | −0.708683 | ||||||||
\(902\) | 3186.03 | 0.117609 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1920.92 | 0.0706736 | ||||||||
\(905\) | 4367.48 | 0.160420 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3667.46 | −0.134263 | −0.0671313 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671313 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(908\) | −865.992 | −0.0316508 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28307.6 | 1.03119 | ||||||||
\(911\) | −21457.9 | −0.780385 | −0.390192 | − | 0.920733i | \(-0.627591\pi\) | ||||
−0.390192 | + | 0.920733i | \(0.627591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12536.1 | 0.454420 | ||||||||
\(914\) | 15513.8 | 0.561433 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3698.66 | −0.133414 | ||||||||
\(917\) | −26431.8 | −0.951859 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11109.3 | −0.398762 | −0.199381 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199381 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14128.4 | −0.504657 | ||||||||
\(923\) | −58637.9 | −2.09110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9205.02 | 0.327199 | ||||||||
\(926\) | 25199.3 | 0.894279 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.7655 | 0.000946790 0 | ||||||||
\(929\) | 20804.3 | 0.734732 | 0.367366 | − | 0.930076i | \(-0.380260\pi\) | ||||
0.367366 | + | 0.930076i | \(0.380260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −100892. | −3.55166 | ||||||||
\(932\) | 9478.75 | 0.333140 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29492.0 | −1.03320 | ||||||||
\(935\) | 3893.20 | 0.136173 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35550.5 | −1.23947 | −0.619735 | − | 0.784811i | \(-0.712760\pi\) | ||||
−0.619735 | + | 0.784811i | \(0.712760\pi\) | |||||||
\(938\) | 58097.5 | 2.02234 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10700.7 | 0.371297 | ||||||||
\(941\) | −49674.4 | −1.72087 | −0.860436 | − | 0.509558i | \(-0.829809\pi\) | ||||
−0.860436 | + | 0.509558i | \(0.829809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2203.23 | 0.0760839 | ||||||||
\(944\) | 5647.20 | 0.194704 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11040.9 | 0.379462 | ||||||||
\(947\) | −33466.2 | −1.14837 | −0.574184 | − | 0.818726i | \(-0.694681\pi\) | ||||
−0.574184 | + | 0.818726i | \(0.694681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7308.85 | 0.250006 | ||||||||
\(950\) | −5532.67 | −0.188951 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13268.5 | −0.451718 | ||||||||
\(953\) | 17298.4 | 0.587984 | 0.293992 | − | 0.955808i | \(-0.405016\pi\) | ||||
0.293992 | + | 0.955808i | \(0.405016\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12488.7 | 0.423167 | ||||||||
\(956\) | 11078.4 | 0.374791 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34822.5 | 1.17439 | ||||||||
\(959\) | −85726.0 | −2.88659 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15430.4 | −0.517955 | ||||||||
\(962\) | −58848.2 | −1.97229 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21336.4 | −0.712862 | ||||||||
\(965\) | 4545.78 | 0.151641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14869.7 | −0.494495 | −0.247248 | − | 0.968952i | \(-0.579526\pi\) | ||||
−0.247248 | + | 0.968952i | \(0.579526\pi\) | |||||||
\(968\) | −8435.59 | −0.280093 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2719.28 | −0.0900113 | ||||||||
\(971\) | −26634.9 | −0.880283 | −0.440142 | − | 0.897928i | \(-0.645072\pi\) | ||||
−0.440142 | + | 0.897928i | \(0.645072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32731.8 | −1.07845 | ||||||||
\(974\) | 2640.69 | 0.0868717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8115.57 | −0.266161 | ||||||||
\(977\) | −40803.6 | −1.33615 | −0.668077 | − | 0.744092i | \(-0.732882\pi\) | ||||
−0.668077 | + | 0.744092i | \(0.732882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17463.7 | 0.570115 | ||||||||
\(980\) | 18235.6 | 0.594404 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34231.6 | −1.11240 | ||||||||
\(983\) | 18615.8 | 0.604021 | 0.302011 | − | 0.953305i | \(-0.402342\pi\) | ||||
0.302011 | + | 0.953305i | \(0.402342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3043.14 | −0.0984389 | ||||||||
\(986\) | 78.3257 | 0.00252982 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35370.6 | 1.13896 | ||||||||
\(989\) | 7635.11 | 0.245483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46185.1 | 1.48044 | 0.740220 | − | 0.672364i | \(-0.234721\pi\) | ||||
0.740220 | + | 0.672364i | \(0.234721\pi\) | |||||||
\(992\) | −3834.74 | −0.122735 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −51984.5 | −1.65880 | ||||||||
\(995\) | −11524.9 | −0.367200 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16544.3 | 0.525541 | 0.262771 | − | 0.964858i | \(-0.415364\pi\) | ||||
0.262771 | + | 0.964858i | \(0.415364\pi\) | |||||||
\(998\) | 35081.2 | 1.11270 | ||||||||
\(999\) | 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 | 2070.4.a.bj.1.1 | 4 | ||
3.2 | odd | 2 | 230.4.a.h.1.1 | ✓ | 4 | ||
12.11 | even | 2 | 1840.4.a.m.1.4 | 4 | |||
15.2 | even | 4 | 1150.4.b.n.599.4 | 8 | |||
15.8 | even | 4 | 1150.4.b.n.599.5 | 8 | |||
15.14 | odd | 2 | 1150.4.a.p.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
1150.4.a.p.1.4 | 4 | 15.14 | odd | 2 | |||
1150.4.b.n.599.4 | 8 | 15.2 | even | 4 | |||
1150.4.b.n.599.5 | 8 | 15.8 | even | 4 | |||
1840.4.a.m.1.4 | 4 | 12.11 | even | 2 | |||
2070.4.a.bj.1.1 | 4 | 1.1 | even | 1 | trivial |