Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 23x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.52356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52356 | 0.538658 | 0.269329 | − | 0.963048i | \(-0.413198\pi\) | ||||
0.269329 | + | 0.963048i | \(0.413198\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.67878 | −0.709847 | ||||||||
\(5\) | −9.65841 | −0.863874 | −0.431937 | − | 0.901904i | \(-0.642170\pi\) | ||||
−0.431937 | + | 0.901904i | \(0.642170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.3639 | 1.20754 | 0.603769 | − | 0.797159i | \(-0.293665\pi\) | ||||
0.603769 | + | 0.797159i | \(0.293665\pi\) | |||||||
\(8\) | −20.8404 | −0.921023 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.7151 | −0.465333 | ||||||||
\(11\) | 50.3050 | 1.37887 | 0.689433 | − | 0.724349i | \(-0.257860\pi\) | ||||
0.689433 | + | 0.724349i | \(0.257860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 34.0727 | 0.650450 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.6788 | 0.213731 | ||||||||
\(17\) | −86.1454 | −1.22902 | −0.614509 | − | 0.788910i | \(-0.710646\pi\) | ||||
−0.614509 | + | 0.788910i | \(0.710646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.880 | 1.41127 | 0.705633 | − | 0.708578i | \(-0.250663\pi\) | ||||
0.705633 | + | 0.708578i | \(0.250663\pi\) | |||||||
\(20\) | 54.8480 | 0.613219 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 76.6424 | 0.742737 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −31.7151 | −0.253721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −127.000 | −0.857168 | ||||||||
\(29\) | −14.1454 | −0.0905768 | −0.0452884 | − | 0.998974i | \(-0.514421\pi\) | ||||
−0.0452884 | + | 0.998974i | \(0.514421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −196.215 | −1.13682 | −0.568408 | − | 0.822747i | \(-0.692441\pi\) | ||||
−0.568408 | + | 0.822747i | \(0.692441\pi\) | |||||||
\(32\) | 187.563 | 1.03615 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −131.247 | −0.662021 | ||||||||
\(35\) | −216.000 | −1.04316 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −154.424 | −0.686138 | −0.343069 | − | 0.939310i | \(-0.611467\pi\) | ||||
−0.343069 | + | 0.939310i | \(0.611467\pi\) | |||||||
\(38\) | 178.073 | 0.760190 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 201.285 | 0.795648 | ||||||||
\(41\) | 265.726 | 1.01218 | 0.506091 | − | 0.862480i | \(-0.331090\pi\) | ||||
0.506091 | + | 0.862480i | \(0.331090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 211.855 | 0.751338 | 0.375669 | − | 0.926754i | \(-0.377413\pi\) | ||||
0.375669 | + | 0.926754i | \(0.377413\pi\) | |||||||
\(44\) | −285.671 | −0.978785 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −109.696 | −0.351604 | ||||||||
\(47\) | −67.5535 | −0.209653 | −0.104827 | − | 0.994491i | \(-0.533429\pi\) | ||||
−0.104827 | + | 0.994491i | \(0.533429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 157.145 | 0.458150 | ||||||||
\(50\) | −48.3197 | −0.136669 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −686.581 | −1.77942 | −0.889710 | − | 0.456527i | \(-0.849093\pi\) | ||||
−0.889710 | + | 0.456527i | \(0.849093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −485.866 | −1.19117 | ||||||||
\(56\) | −466.073 | −1.11217 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −21.5512 | −0.0487899 | ||||||||
\(59\) | 91.9304 | 0.202853 | 0.101426 | − | 0.994843i | \(-0.467659\pi\) | ||||
0.101426 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 329.006 | 0.690572 | 0.345286 | − | 0.938498i | \(-0.387782\pi\) | ||||
0.345286 | + | 0.938498i | \(0.387782\pi\) | |||||||
\(62\) | −298.945 | −0.612355 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 176.333 | 0.344400 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 768.370 | 1.40106 | 0.700532 | − | 0.713621i | \(-0.252946\pi\) | ||||
0.700532 | + | 0.713621i | \(0.252946\pi\) | |||||||
\(68\) | 489.201 | 0.872416 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −329.088 | −0.561908 | ||||||||
\(71\) | −264.969 | −0.442902 | −0.221451 | − | 0.975171i | \(-0.571079\pi\) | ||||
−0.221451 | + | 0.975171i | \(0.571079\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 771.306 | 1.23664 | 0.618319 | − | 0.785927i | \(-0.287814\pi\) | ||||
0.618319 | + | 0.785927i | \(0.287814\pi\) | |||||||
\(74\) | −235.273 | −0.369594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −663.734 | −1.00178 | ||||||||
\(77\) | 1125.02 | 1.66503 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1226.86 | 1.74725 | 0.873624 | − | 0.486602i | \(-0.161764\pi\) | ||||
0.873624 | + | 0.486602i | \(0.161764\pi\) | |||||||
\(80\) | −132.115 | −0.184637 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 404.849 | 0.545220 | ||||||||
\(83\) | 514.019 | 0.679771 | 0.339885 | − | 0.940467i | \(-0.389612\pi\) | ||||
0.339885 | + | 0.940467i | \(0.389612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 832.027 | 1.06172 | ||||||||
\(86\) | 322.772 | 0.404714 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1048.38 | −1.26997 | ||||||||
\(89\) | −527.889 | −0.628720 | −0.314360 | − | 0.949304i | \(-0.601790\pi\) | ||||
−0.314360 | + | 0.949304i | \(0.601790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 408.872 | 0.463346 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −102.921 | −0.112931 | ||||||||
\(95\) | −1128.87 | −1.21916 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −74.2755 | −0.0777478 | −0.0388739 | − | 0.999244i | \(-0.512377\pi\) | ||||
−0.0388739 | + | 0.999244i | \(0.512377\pi\) | |||||||
\(98\) | 239.420 | 0.246786 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 180.103 | 0.180103 | ||||||||
\(101\) | −609.419 | −0.600390 | −0.300195 | − | 0.953878i | \(-0.597052\pi\) | ||||
−0.300195 | + | 0.953878i | \(0.597052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32.4361 | −0.0310293 | −0.0155147 | − | 0.999880i | \(-0.504939\pi\) | ||||
−0.0155147 | + | 0.999880i | \(0.504939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1046.04 | −0.958498 | ||||||||
\(107\) | 1725.45 | 1.55893 | 0.779467 | − | 0.626444i | \(-0.215490\pi\) | ||||
0.779467 | + | 0.626444i | \(0.215490\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1273.43 | 1.11902 | 0.559508 | − | 0.828825i | \(-0.310990\pi\) | ||||
0.559508 | + | 0.828825i | \(0.310990\pi\) | |||||||
\(110\) | −740.244 | −0.641632 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 305.911 | 0.258088 | ||||||||
\(113\) | −1114.73 | −0.928006 | −0.464003 | − | 0.885834i | \(-0.653587\pi\) | ||||
−0.464003 | + | 0.885834i | \(0.653587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 695.406 | 0.563886 | ||||||||
\(116\) | 80.3284 | 0.0642957 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140.061 | 0.109268 | ||||||||
\(119\) | −1926.55 | −1.48409 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1199.59 | 0.901272 | ||||||||
\(122\) | 501.259 | 0.371982 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1114.26 | 0.806966 | ||||||||
\(125\) | 1513.62 | 1.08306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1174.01 | 0.820289 | 0.410144 | − | 0.912021i | \(-0.365478\pi\) | ||||
0.410144 | + | 0.912021i | \(0.365478\pi\) | |||||||
\(128\) | −1231.85 | −0.850637 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1445.16 | 0.963851 | 0.481925 | − | 0.876212i | \(-0.339938\pi\) | ||||
0.481925 | + | 0.876212i | \(0.339938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2613.89 | 1.70416 | ||||||||
\(134\) | 1170.65 | 0.754695 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1795.30 | 1.13195 | ||||||||
\(137\) | −508.793 | −0.317293 | −0.158646 | − | 0.987335i | \(-0.550713\pi\) | ||||
−0.158646 | + | 0.987335i | \(0.550713\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −757.018 | −0.461938 | −0.230969 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230969 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(140\) | 1226.62 | 0.740486 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −403.695 | −0.238573 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 136.622 | 0.0782470 | ||||||||
\(146\) | 1175.13 | 0.666125 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 876.939 | 0.487054 | ||||||||
\(149\) | 3247.79 | 1.78570 | 0.892851 | − | 0.450352i | \(-0.148702\pi\) | ||||
0.892851 | + | 0.450352i | \(0.148702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 795.296 | 0.428611 | 0.214305 | − | 0.976767i | \(-0.431251\pi\) | ||||
0.214305 | + | 0.976767i | \(0.431251\pi\) | |||||||
\(152\) | −2435.82 | −1.29981 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1714.03 | 0.896884 | ||||||||
\(155\) | 1895.13 | 0.982067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.2732 | −0.0331807 | −0.0165903 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165903 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(158\) | 1869.19 | 0.941169 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1811.56 | −0.895104 | ||||||||
\(161\) | −1610.20 | −0.788210 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1855.39 | −0.891568 | −0.445784 | − | 0.895140i | \(-0.647075\pi\) | ||||
−0.445784 | + | 0.895140i | \(0.647075\pi\) | |||||||
\(164\) | −1509.00 | −0.718495 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 783.137 | 0.366164 | ||||||||
\(167\) | 3532.54 | 1.63686 | 0.818432 | − | 0.574604i | \(-0.194844\pi\) | ||||
0.818432 | + | 0.574604i | \(0.194844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1267.64 | 0.571903 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1203.08 | −0.533335 | ||||||||
\(173\) | 3178.36 | 1.39680 | 0.698400 | − | 0.715708i | \(-0.253896\pi\) | ||||
0.698400 | + | 0.715708i | \(0.253896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −709.275 | −0.306378 | ||||||||
\(176\) | 688.111 | 0.294706 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −804.267 | −0.338665 | ||||||||
\(179\) | −2741.16 | −1.14460 | −0.572302 | − | 0.820043i | \(-0.693950\pi\) | ||||
−0.572302 | + | 0.820043i | \(0.693950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3871.09 | 1.58970 | 0.794850 | − | 0.606806i | \(-0.207550\pi\) | ||||
0.794850 | + | 0.606806i | \(0.207550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1500.51 | 0.601189 | ||||||||
\(185\) | 1491.49 | 0.592737 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4333.54 | −1.69465 | ||||||||
\(188\) | 383.621 | 0.148822 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1719.90 | −0.656708 | ||||||||
\(191\) | 928.291 | 0.351669 | 0.175834 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175834 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2261.51 | −0.843456 | −0.421728 | − | 0.906722i | \(-0.638576\pi\) | ||||
−0.421728 | + | 0.906722i | \(0.638576\pi\) | |||||||
\(194\) | −113.163 | −0.0418795 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −892.394 | −0.325216 | ||||||||
\(197\) | 2265.59 | 0.819374 | 0.409687 | − | 0.912226i | \(-0.365638\pi\) | ||||
0.409687 | + | 0.912226i | \(0.365638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −260.895 | −0.0929366 | −0.0464683 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464683 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(200\) | 660.955 | 0.233683 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −928.483 | −0.323405 | ||||||||
\(203\) | −316.346 | −0.109375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2566.49 | −0.874399 | ||||||||
\(206\) | −49.4181 | −0.0167142 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5879.63 | 1.94595 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5851.22 | 1.90907 | 0.954537 | − | 0.298092i | \(-0.0963502\pi\) | ||||
0.954537 | + | 0.298092i | \(0.0963502\pi\) | |||||||
\(212\) | 3898.94 | 1.26312 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2628.82 | 0.839732 | ||||||||
\(215\) | −2046.18 | −0.649062 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4388.15 | −1.37275 | ||||||||
\(218\) | 1940.15 | 0.602767 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2759.13 | 0.845547 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3463.60 | −1.04009 | −0.520045 | − | 0.854139i | \(-0.674085\pi\) | ||||
−0.520045 | + | 0.854139i | \(0.674085\pi\) | |||||||
\(224\) | 4194.65 | 1.25119 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1698.35 | −0.499878 | ||||||||
\(227\) | −5329.15 | −1.55819 | −0.779093 | − | 0.626908i | \(-0.784320\pi\) | ||||
−0.779093 | + | 0.626908i | \(0.784320\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4773.95 | 1.37761 | 0.688803 | − | 0.724949i | \(-0.258137\pi\) | ||||
0.688803 | + | 0.724949i | \(0.258137\pi\) | |||||||
\(230\) | 1059.49 | 0.303742 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 294.795 | 0.0834233 | ||||||||
\(233\) | 4813.78 | 1.35348 | 0.676741 | − | 0.736221i | \(-0.263392\pi\) | ||||
0.676741 | + | 0.736221i | \(0.263392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 652.459 | 0.181114 | ||||||||
\(236\) | −522.052 | −0.143995 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2935.20 | −0.799416 | ||||||||
\(239\) | −1683.19 | −0.455549 | −0.227775 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227775 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −664.861 | −0.177707 | −0.0888537 | − | 0.996045i | \(-0.528320\pi\) | ||||
−0.0888537 | + | 0.996045i | \(0.528320\pi\) | |||||||
\(242\) | 1827.65 | 0.485477 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1868.35 | −0.490201 | ||||||||
\(245\) | −1517.77 | −0.395784 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4089.20 | 1.04703 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2306.08 | 0.583398 | ||||||||
\(251\) | −2142.04 | −0.538662 | −0.269331 | − | 0.963048i | \(-0.586802\pi\) | ||||
−0.269331 | + | 0.963048i | \(0.586802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3621.96 | −0.900042 | ||||||||
\(254\) | 1788.67 | 0.441855 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3287.46 | −0.802603 | ||||||||
\(257\) | −3152.62 | −0.765194 | −0.382597 | − | 0.923915i | \(-0.624970\pi\) | ||||
−0.382597 | + | 0.923915i | \(0.624970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3453.52 | −0.828539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2201.79 | 0.519186 | ||||||||
\(263\) | 2167.71 | 0.508238 | 0.254119 | − | 0.967173i | \(-0.418214\pi\) | ||||
0.254119 | + | 0.967173i | \(0.418214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6631.28 | 1.53719 | ||||||||
\(266\) | 3982.40 | 0.917958 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4363.40 | −0.994542 | ||||||||
\(269\) | 3248.98 | 0.736409 | 0.368204 | − | 0.929745i | \(-0.379973\pi\) | ||||
0.368204 | + | 0.929745i | \(0.379973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4897.70 | −1.09784 | −0.548919 | − | 0.835876i | \(-0.684960\pi\) | ||||
−0.548919 | + | 0.835876i | \(0.684960\pi\) | |||||||
\(272\) | −1178.36 | −0.262679 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −775.175 | −0.170912 | ||||||||
\(275\) | −1595.43 | −0.349847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2900.33 | 0.629111 | 0.314555 | − | 0.949239i | \(-0.398145\pi\) | ||||
0.314555 | + | 0.949239i | \(0.398145\pi\) | |||||||
\(278\) | −1153.36 | −0.248827 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4501.52 | 0.960776 | ||||||||
\(281\) | −4396.53 | −0.933364 | −0.466682 | − | 0.884425i | \(-0.654551\pi\) | ||||
−0.466682 | + | 0.884425i | \(0.654551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −559.151 | −0.117449 | −0.0587245 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587245 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(284\) | 1504.70 | 0.314393 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5942.69 | 1.22225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2508.02 | 0.510487 | ||||||||
\(290\) | 208.151 | 0.0421484 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4380.08 | −0.877825 | ||||||||
\(293\) | 6918.65 | 1.37950 | 0.689748 | − | 0.724050i | \(-0.257722\pi\) | ||||
0.689748 | + | 0.724050i | \(0.257722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −887.901 | −0.175239 | ||||||||
\(296\) | 3218.25 | 0.631949 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4948.19 | 0.961883 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4737.90 | 0.907270 | ||||||||
\(302\) | 1211.68 | 0.230875 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1598.77 | 0.301631 | ||||||||
\(305\) | −3177.67 | −0.596567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8980.94 | −1.66961 | −0.834803 | − | 0.550548i | \(-0.814419\pi\) | ||||
−0.834803 | + | 0.550548i | \(0.814419\pi\) | |||||||
\(308\) | −6388.73 | −1.18192 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2887.33 | 0.528998 | ||||||||
\(311\) | 7943.13 | 1.44827 | 0.724137 | − | 0.689656i | \(-0.242238\pi\) | ||||
0.724137 | + | 0.689656i | \(0.242238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5059.57 | −0.913686 | −0.456843 | − | 0.889547i | \(-0.651020\pi\) | ||||
−0.456843 | + | 0.889547i | \(0.651020\pi\) | |||||||
\(314\) | −99.4473 | −0.0178730 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6967.07 | −1.24028 | ||||||||
\(317\) | 8702.12 | 1.54183 | 0.770914 | − | 0.636939i | \(-0.219800\pi\) | ||||
0.770914 | + | 0.636939i | \(0.219800\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −711.582 | −0.124893 | ||||||||
\(320\) | −1703.10 | −0.297519 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2453.23 | −0.424576 | ||||||||
\(323\) | −10068.6 | −1.73447 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2826.79 | −0.480250 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5537.84 | −0.932244 | ||||||||
\(329\) | −1510.76 | −0.253164 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1737.65 | −0.288549 | −0.144275 | − | 0.989538i | \(-0.546085\pi\) | ||||
−0.144275 | + | 0.989538i | \(0.546085\pi\) | |||||||
\(332\) | −2919.00 | −0.482533 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5382.02 | 0.881710 | ||||||||
\(335\) | −7421.23 | −1.21034 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2917.47 | 0.471586 | 0.235793 | − | 0.971803i | \(-0.424231\pi\) | ||||
0.235793 | + | 0.971803i | \(0.424231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4724.90 | −0.753658 | ||||||||
\(341\) | −9870.61 | −1.56752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4156.44 | −0.654305 | ||||||||
\(344\) | −4415.13 | −0.692000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4842.41 | 0.752397 | ||||||||
\(347\) | −5081.23 | −0.786095 | −0.393047 | − | 0.919518i | \(-0.628579\pi\) | ||||
−0.393047 | + | 0.919518i | \(0.628579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4266.14 | 0.654330 | 0.327165 | − | 0.944967i | \(-0.393907\pi\) | ||||
0.327165 | + | 0.944967i | \(0.393907\pi\) | |||||||
\(350\) | −1080.62 | −0.165033 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9435.38 | 1.42871 | ||||||||
\(353\) | −3264.49 | −0.492213 | −0.246106 | − | 0.969243i | \(-0.579151\pi\) | ||||
−0.246106 | + | 0.969243i | \(0.579151\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2559.18 | 0.382612 | ||||||||
\(356\) | 2997.76 | 0.446295 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4176.31 | −0.616550 | ||||||||
\(359\) | 4416.98 | 0.649357 | 0.324679 | − | 0.945824i | \(-0.394744\pi\) | ||||
0.324679 | + | 0.945824i | \(0.394744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6801.87 | 0.991670 | ||||||||
\(362\) | 5897.82 | 0.856305 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7449.59 | −1.06830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1740.22 | −0.247516 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(368\) | −984.872 | −0.139511 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2272.37 | 0.319283 | ||||||||
\(371\) | −15354.7 | −2.14872 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1176.28 | 0.163285 | 0.0816427 | − | 0.996662i | \(-0.473983\pi\) | ||||
0.0816427 | + | 0.996662i | \(0.473983\pi\) | |||||||
\(374\) | −6602.39 | −0.912838 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1407.84 | 0.193095 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7135.54 | −0.967092 | −0.483546 | − | 0.875319i | \(-0.660651\pi\) | ||||
−0.483546 | + | 0.875319i | \(0.660651\pi\) | |||||||
\(380\) | 6410.62 | 0.865415 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1414.30 | 0.189429 | ||||||||
\(383\) | −1942.87 | −0.259207 | −0.129603 | − | 0.991566i | \(-0.541370\pi\) | ||||
−0.129603 | + | 0.991566i | \(0.541370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10865.9 | −1.43838 | ||||||||
\(386\) | −3445.53 | −0.454334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 421.794 | 0.0551891 | ||||||||
\(389\) | 7545.92 | 0.983531 | 0.491766 | − | 0.870728i | \(-0.336352\pi\) | ||||
0.491766 | + | 0.870728i | \(0.336352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6202.47 | 0.802231 | ||||||||
\(392\) | −3274.97 | −0.421967 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3451.75 | 0.441362 | ||||||||
\(395\) | −11849.5 | −1.50940 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −415.922 | −0.0525806 | −0.0262903 | − | 0.999654i | \(-0.508369\pi\) | ||||
−0.0262903 | + | 0.999654i | \(0.508369\pi\) | |||||||
\(398\) | −397.489 | −0.0500611 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −433.824 | −0.0542280 | ||||||||
\(401\) | −958.178 | −0.119324 | −0.0596622 | − | 0.998219i | \(-0.519002\pi\) | ||||
−0.0596622 | + | 0.998219i | \(0.519002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3460.75 | 0.426185 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −481.970 | −0.0589157 | ||||||||
\(407\) | −7768.29 | −0.946093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4284.83 | −0.518022 | −0.259011 | − | 0.965874i | \(-0.583397\pi\) | ||||
−0.259011 | + | 0.965874i | \(0.583397\pi\) | |||||||
\(410\) | −3910.20 | −0.471002 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 184.197 | 0.0220261 | ||||||||
\(413\) | 2055.92 | 0.244953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4964.61 | −0.587236 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8957.95 | 1.04820 | ||||||||
\(419\) | 9949.01 | 1.16000 | 0.580001 | − | 0.814616i | \(-0.303052\pi\) | ||||
0.580001 | + | 0.814616i | \(0.303052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 377.250 | 0.0436724 | 0.0218362 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218362 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(422\) | 8914.66 | 1.02834 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14308.6 | 1.63889 | ||||||||
\(425\) | 2732.11 | 0.311828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7357.86 | 0.833892 | ||||||||
\(428\) | −9798.47 | −1.10661 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3117.47 | −0.349622 | ||||||||
\(431\) | 2437.13 | 0.272373 | 0.136186 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136186 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11215.1 | 1.24471 | 0.622357 | − | 0.782733i | \(-0.286175\pi\) | ||||
0.622357 | + | 0.782733i | \(0.286175\pi\) | |||||||
\(434\) | −6685.58 | −0.739443 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7231.55 | −0.794331 | ||||||||
\(437\) | −8415.34 | −0.921191 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1835.19 | −0.199519 | −0.0997596 | − | 0.995012i | \(-0.531807\pi\) | ||||
−0.0997596 | + | 0.995012i | \(0.531807\pi\) | |||||||
\(440\) | 10125.6 | 1.09709 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11610.1 | −1.24518 | −0.622588 | − | 0.782550i | \(-0.713919\pi\) | ||||
−0.622588 | + | 0.782550i | \(0.713919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5098.56 | 0.543135 | ||||||||
\(446\) | −5276.99 | −0.560253 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3943.50 | 0.415877 | ||||||||
\(449\) | 14087.0 | 1.48064 | 0.740319 | − | 0.672255i | \(-0.234674\pi\) | ||||
0.740319 | + | 0.672255i | \(0.234674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13367.4 | 1.39566 | ||||||||
\(452\) | 6330.29 | 0.658743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8119.26 | −0.839330 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2375.01 | 0.243103 | 0.121552 | − | 0.992585i | \(-0.461213\pi\) | ||||
0.121552 | + | 0.992585i | \(0.461213\pi\) | |||||||
\(458\) | 7273.38 | 0.742058 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3949.05 | −0.400273 | ||||||||
\(461\) | 6372.06 | 0.643766 | 0.321883 | − | 0.946779i | \(-0.395684\pi\) | ||||
0.321883 | + | 0.946779i | \(0.395684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −63.4732 | −0.00637117 | −0.00318558 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318558 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(464\) | −193.491 | −0.0193591 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7334.06 | 0.729064 | ||||||||
\(467\) | 7855.78 | 0.778420 | 0.389210 | − | 0.921149i | \(-0.372748\pi\) | ||||
0.389210 | + | 0.921149i | \(0.372748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17183.8 | 1.69184 | ||||||||
\(470\) | 994.058 | 0.0975584 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1915.86 | −0.186832 | ||||||||
\(473\) | 10657.3 | 1.03599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3706.85 | −0.358068 | ||||||||
\(476\) | 10940.4 | 1.05348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2564.43 | −0.245385 | ||||||||
\(479\) | 13033.3 | 1.24323 | 0.621613 | − | 0.783324i | \(-0.286477\pi\) | ||||
0.621613 | + | 0.783324i | \(0.286477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1012.95 | −0.0957235 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6812.23 | −0.639766 | ||||||||
\(485\) | 717.384 | 0.0671643 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −69.8976 | −0.00650383 | −0.00325191 | − | 0.999995i | \(-0.501035\pi\) | ||||
−0.00325191 | + | 0.999995i | \(0.501035\pi\) | |||||||
\(488\) | −6856.60 | −0.636033 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2312.41 | −0.213192 | ||||||||
\(491\) | 2625.66 | 0.241333 | 0.120667 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120667 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1218.56 | 0.111321 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2683.99 | −0.242973 | ||||||||
\(497\) | −5925.75 | −0.534821 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7631.34 | 0.684621 | 0.342310 | − | 0.939587i | \(-0.388791\pi\) | ||||
0.342310 | + | 0.939587i | \(0.388791\pi\) | |||||||
\(500\) | −8595.51 | −0.768806 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3263.51 | −0.290154 | ||||||||
\(503\) | 4320.14 | 0.382953 | 0.191477 | − | 0.981497i | \(-0.438672\pi\) | ||||
0.191477 | + | 0.981497i | \(0.438672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5886.01 | 0.518662 | ||||||||
\(506\) | −5518.26 | −0.484815 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6666.95 | −0.582280 | ||||||||
\(509\) | 12450.7 | 1.08422 | 0.542109 | − | 0.840308i | \(-0.317626\pi\) | ||||
0.542109 | + | 0.840308i | \(0.317626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17249.4 | 1.49329 | ||||||||
\(512\) | 4846.21 | 0.418309 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4803.18 | −0.412178 | ||||||||
\(515\) | 313.281 | 0.0268054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3398.28 | −0.289083 | ||||||||
\(518\) | −5261.63 | −0.446299 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14373.1 | −1.20863 | −0.604314 | − | 0.796746i | \(-0.706553\pi\) | ||||
−0.604314 | + | 0.796746i | \(0.706553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16946.7 | −1.41688 | −0.708439 | − | 0.705772i | \(-0.750600\pi\) | ||||
−0.708439 | + | 0.705772i | \(0.750600\pi\) | |||||||
\(524\) | −8206.76 | −0.684187 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3302.62 | 0.273767 | ||||||||
\(527\) | 16903.0 | 1.39717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 10103.1 | 0.828022 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14843.7 | −1.20969 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16665.1 | −1.34672 | ||||||||
\(536\) | −16013.1 | −1.29041 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4950.00 | 0.396673 | ||||||||
\(539\) | 7905.20 | 0.631727 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 815.667 | 0.0648212 | 0.0324106 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324106 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(542\) | −7461.92 | −0.591359 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16157.7 | −1.27345 | ||||||||
\(545\) | −12299.3 | −0.966689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17971.4 | −1.40476 | −0.702378 | − | 0.711804i | \(-0.747878\pi\) | ||||
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(548\) | 2889.32 | 0.225230 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2430.72 | −0.188448 | ||||||||
\(551\) | −1653.31 | −0.127828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27437.4 | 2.10987 | ||||||||
\(554\) | 4418.81 | 0.338876 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4298.94 | 0.327906 | ||||||||
\(557\) | −6760.83 | −0.514301 | −0.257151 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257151 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2954.62 | −0.222956 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6698.36 | −0.502764 | ||||||||
\(563\) | 12962.7 | 0.970359 | 0.485179 | − | 0.874415i | \(-0.338754\pi\) | ||||
0.485179 | + | 0.874415i | \(0.338754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10766.5 | 0.801681 | ||||||||
\(566\) | −851.898 | −0.0632649 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5522.05 | 0.407923 | ||||||||
\(569\) | 164.757 | 0.0121388 | 0.00606938 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00606938 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5216.55 | 0.382322 | 0.191161 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191161 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9054.01 | 0.658375 | ||||||||
\(575\) | 2283.49 | 0.165614 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12753.3 | 0.920151 | 0.460076 | − | 0.887880i | \(-0.347822\pi\) | ||||
0.460076 | + | 0.887880i | \(0.347822\pi\) | |||||||
\(578\) | 3821.11 | 0.274978 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −775.844 | −0.0555434 | ||||||||
\(581\) | 11495.5 | 0.820849 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34538.5 | −2.45358 | ||||||||
\(584\) | −16074.3 | −1.13897 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10540.9 | 0.743076 | ||||||||
\(587\) | −1575.38 | −0.110771 | −0.0553857 | − | 0.998465i | \(-0.517639\pi\) | ||||
−0.0553857 | + | 0.998465i | \(0.517639\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22933.6 | −1.60435 | ||||||||
\(590\) | −1352.77 | −0.0943941 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2112.33 | −0.146649 | ||||||||
\(593\) | −3845.95 | −0.266331 | −0.133165 | − | 0.991094i | \(-0.542514\pi\) | ||||
−0.133165 | + | 0.991094i | \(0.542514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18607.4 | 1.28207 | ||||||||
\(596\) | −18443.5 | −1.26758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6107.20 | −0.416583 | −0.208292 | − | 0.978067i | \(-0.566790\pi\) | ||||
−0.208292 | + | 0.978067i | \(0.566790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9638.90 | 0.654208 | 0.327104 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327104 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(602\) | 7218.46 | 0.488708 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4516.31 | −0.304248 | ||||||||
\(605\) | −11586.2 | −0.778586 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11821.7 | 0.790489 | 0.395244 | − | 0.918576i | \(-0.370660\pi\) | ||||
0.395244 | + | 0.918576i | \(0.370660\pi\) | |||||||
\(608\) | 21922.4 | 1.46228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4841.36 | −0.321346 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8107.86 | 0.534214 | 0.267107 | − | 0.963667i | \(-0.413932\pi\) | ||||
0.267107 | + | 0.963667i | \(0.413932\pi\) | |||||||
\(614\) | −13683.0 | −0.899347 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23445.8 | −1.53354 | ||||||||
\(617\) | −27647.6 | −1.80397 | −0.901985 | − | 0.431768i | \(-0.857890\pi\) | ||||
−0.901985 | + | 0.431768i | \(0.857890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29181.9 | 1.89486 | 0.947432 | − | 0.319956i | \(-0.103668\pi\) | ||||
0.947432 | + | 0.319956i | \(0.103668\pi\) | |||||||
\(620\) | −10762.0 | −0.697118 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12101.8 | 0.780125 | ||||||||
\(623\) | −11805.7 | −0.759204 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10654.8 | −0.681905 | ||||||||
\(626\) | −7708.53 | −0.492165 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 370.672 | 0.0235532 | ||||||||
\(629\) | 13302.9 | 0.843277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2209.34 | −0.139386 | −0.0696928 | − | 0.997569i | \(-0.522202\pi\) | ||||
−0.0696928 | + | 0.997569i | \(0.522202\pi\) | |||||||
\(632\) | −25568.2 | −1.60926 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13258.2 | 0.830518 | ||||||||
\(635\) | −11339.1 | −0.708627 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1084.13 | −0.0672748 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11897.8 | 0.734844 | ||||||||
\(641\) | 18256.0 | 1.12491 | 0.562455 | − | 0.826828i | \(-0.309857\pi\) | ||||
0.562455 | + | 0.826828i | \(0.309857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1281.61 | 0.0786033 | 0.0393016 | − | 0.999227i | \(-0.487487\pi\) | ||||
0.0393016 | + | 0.999227i | \(0.487487\pi\) | |||||||
\(644\) | 9143.99 | 0.559509 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15340.1 | −0.934287 | ||||||||
\(647\) | −16393.2 | −0.996107 | −0.498054 | − | 0.867146i | \(-0.665952\pi\) | ||||
−0.498054 | + | 0.867146i | \(0.665952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4624.56 | 0.279707 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10536.4 | 0.632878 | ||||||||
\(653\) | −16759.2 | −1.00434 | −0.502172 | − | 0.864768i | \(-0.667466\pi\) | ||||
−0.502172 | + | 0.864768i | \(0.667466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13958.0 | −0.832646 | ||||||||
\(656\) | 3634.81 | 0.216335 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2301.73 | −0.136369 | ||||||||
\(659\) | 29659.3 | 1.75320 | 0.876601 | − | 0.481217i | \(-0.159805\pi\) | ||||
0.876601 | + | 0.481217i | \(0.159805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10386.0 | −0.611147 | −0.305573 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305573 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(662\) | −2647.40 | −0.155429 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10712.4 | −0.626084 | ||||||||
\(665\) | −25246.0 | −1.47218 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1018.47 | 0.0591232 | ||||||||
\(668\) | −20060.5 | −1.16192 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11306.7 | −0.651962 | ||||||||
\(671\) | 16550.6 | 0.952206 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19449.6 | −1.11400 | −0.557002 | − | 0.830511i | \(-0.688049\pi\) | ||||
−0.557002 | + | 0.830511i | \(0.688049\pi\) | |||||||
\(674\) | 4444.92 | 0.254024 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6629.48 | 0.376354 | 0.188177 | − | 0.982135i | \(-0.439742\pi\) | ||||
0.188177 | + | 0.982135i | \(0.439742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1661.09 | −0.0938835 | ||||||||
\(680\) | −17339.8 | −0.977867 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15038.4 | −0.844356 | ||||||||
\(683\) | 2526.40 | 0.141537 | 0.0707687 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707687 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4914.13 | 0.274101 | ||||||||
\(686\) | −6332.57 | −0.352447 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2897.91 | 0.160584 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3808.76 | 0.209685 | 0.104842 | − | 0.994489i | \(-0.466566\pi\) | ||||
0.104842 | + | 0.994489i | \(0.466566\pi\) | |||||||
\(692\) | −18049.2 | −0.991515 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7741.54 | −0.423436 | ||||||||
\(695\) | 7311.59 | 0.399056 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22891.1 | −1.24399 | ||||||||
\(698\) | 6499.69 | 0.352460 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4027.81 | 0.217482 | ||||||||
\(701\) | −33617.8 | −1.81131 | −0.905655 | − | 0.424015i | \(-0.860620\pi\) | ||||
−0.905655 | + | 0.424015i | \(0.860620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18049.0 | −0.968323 | ||||||||
\(704\) | 8870.43 | 0.474882 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4973.63 | −0.265134 | ||||||||
\(707\) | −13629.0 | −0.724994 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26606.5 | 1.40935 | 0.704675 | − | 0.709530i | \(-0.251093\pi\) | ||||
0.704675 | + | 0.709530i | \(0.251093\pi\) | |||||||
\(710\) | 3899.05 | 0.206097 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11001.4 | 0.579066 | ||||||||
\(713\) | 14127.5 | 0.742046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15566.5 | 0.812494 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6729.51 | 0.349781 | ||||||||
\(719\) | 16539.3 | 0.857877 | 0.428939 | − | 0.903334i | \(-0.358888\pi\) | ||||
0.428939 | + | 0.903334i | \(0.358888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −725.398 | −0.0374691 | ||||||||
\(722\) | 10363.0 | 0.534171 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21983.1 | −1.12844 | ||||||||
\(725\) | 448.622 | 0.0229812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12757.5 | −0.650823 | −0.325411 | − | 0.945573i | \(-0.605503\pi\) | ||||
−0.325411 | + | 0.945573i | \(0.605503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11349.9 | −0.575448 | ||||||||
\(731\) | −18250.3 | −0.923408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20523.4 | −1.03417 | −0.517087 | − | 0.855933i | \(-0.672984\pi\) | ||||
−0.517087 | + | 0.855933i | \(0.672984\pi\) | |||||||
\(734\) | −2651.31 | −0.133327 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13504.6 | −0.676338 | ||||||||
\(737\) | 38652.9 | 1.93188 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7462.66 | 0.371473 | 0.185736 | − | 0.982600i | \(-0.440533\pi\) | ||||
0.185736 | + | 0.982600i | \(0.440533\pi\) | |||||||
\(740\) | −8469.84 | −0.420753 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23393.7 | −1.15742 | ||||||||
\(743\) | 18847.8 | 0.930632 | 0.465316 | − | 0.885145i | \(-0.345941\pi\) | ||||
0.465316 | + | 0.885145i | \(0.345941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31368.5 | −1.54262 | ||||||||
\(746\) | 1792.13 | 0.0879549 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24609.2 | 1.20294 | ||||||||
\(749\) | 38587.9 | 1.88247 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20832.6 | −1.01224 | −0.506119 | − | 0.862464i | \(-0.668920\pi\) | ||||
−0.506119 | + | 0.862464i | \(0.668920\pi\) | |||||||
\(752\) | −924.050 | −0.0448093 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7681.29 | −0.370266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20860.9 | −1.00159 | −0.500795 | − | 0.865566i | \(-0.666959\pi\) | ||||
−0.500795 | + | 0.865566i | \(0.666959\pi\) | |||||||
\(758\) | −10871.4 | −0.520932 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23526.1 | 1.12287 | ||||||||
\(761\) | −4464.86 | −0.212682 | −0.106341 | − | 0.994330i | \(-0.533914\pi\) | ||||
−0.106341 | + | 0.994330i | \(0.533914\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28479.0 | 1.35126 | ||||||||
\(764\) | −5271.56 | −0.249631 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2960.08 | −0.139624 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23797.7 | −1.11595 | −0.557977 | − | 0.829857i | \(-0.688422\pi\) | ||||
−0.557977 | + | 0.829857i | \(0.688422\pi\) | |||||||
\(770\) | −16554.8 | −0.774795 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12842.6 | 0.598725 | ||||||||
\(773\) | 29418.7 | 1.36885 | 0.684423 | − | 0.729085i | \(-0.260054\pi\) | ||||
0.684423 | + | 0.729085i | \(0.260054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6222.99 | 0.288434 | ||||||||
\(776\) | 1547.93 | 0.0716075 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11496.6 | 0.529787 | ||||||||
\(779\) | 31058.0 | 1.42846 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13329.3 | −0.610703 | ||||||||
\(782\) | 9449.80 | 0.432128 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2149.56 | 0.0979208 | ||||||||
\(785\) | 630.435 | 0.0286640 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23896.0 | −1.08234 | −0.541170 | − | 0.840913i | \(-0.682018\pi\) | ||||
−0.541170 | + | 0.840913i | \(0.682018\pi\) | |||||||
\(788\) | −12865.8 | −0.581630 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18053.4 | −0.813052 | ||||||||
\(791\) | −24929.7 | −1.12060 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −633.680 | −0.0283230 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1481.57 | 0.0659708 | ||||||||
\(797\) | 1034.67 | 0.0459847 | 0.0229923 | − | 0.999736i | \(-0.492681\pi\) | ||||
0.0229923 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5819.42 | 0.257667 | ||||||||
\(800\) | −5948.59 | −0.262893 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1459.84 | −0.0642751 | ||||||||
\(803\) | 38800.6 | 1.70516 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15552.0 | 0.680914 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12700.5 | 0.552973 | ||||||||
\(809\) | −29557.9 | −1.28455 | −0.642275 | − | 0.766474i | \(-0.722009\pi\) | ||||
−0.642275 | + | 0.766474i | \(0.722009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30268.9 | 1.31058 | 0.655292 | − | 0.755376i | \(-0.272546\pi\) | ||||
0.655292 | + | 0.755376i | \(0.272546\pi\) | |||||||
\(812\) | 1796.46 | 0.0776396 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11835.4 | −0.509621 | ||||||||
\(815\) | 17920.2 | 0.770203 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24761.5 | 1.06034 | ||||||||
\(818\) | −6528.17 | −0.279037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14574.6 | 0.620690 | ||||||||
\(821\) | −39292.7 | −1.67031 | −0.835156 | − | 0.550013i | \(-0.814623\pi\) | ||||
−0.835156 | + | 0.550013i | \(0.814623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25988.8 | −1.10074 | −0.550372 | − | 0.834920i | \(-0.685514\pi\) | ||||
−0.550372 | + | 0.834920i | \(0.685514\pi\) | |||||||
\(824\) | 675.980 | 0.0285787 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3132.31 | 0.131946 | ||||||||
\(827\) | −19585.1 | −0.823508 | −0.411754 | − | 0.911295i | \(-0.635084\pi\) | ||||
−0.411754 | + | 0.911295i | \(0.635084\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 666.472 | 0.0279222 | 0.0139611 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139611 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(830\) | −7563.86 | −0.316320 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13537.3 | −0.563075 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34118.7 | −1.41404 | ||||||||
\(836\) | −33389.1 | −1.38133 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15157.9 | 0.624845 | ||||||||
\(839\) | −36379.7 | −1.49698 | −0.748490 | − | 0.663146i | \(-0.769221\pi\) | ||||
−0.748490 | + | 0.663146i | \(0.769221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24188.9 | −0.991796 | ||||||||
\(842\) | 574.762 | 0.0235245 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33227.8 | −1.35515 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26827.6 | 1.08832 | ||||||||
\(848\) | −9391.60 | −0.380317 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4162.52 | 0.167969 | ||||||||
\(851\) | 11118.5 | 0.447871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39951.4 | 1.60364 | 0.801822 | − | 0.597563i | \(-0.203864\pi\) | ||||
0.801822 | + | 0.597563i | \(0.203864\pi\) | |||||||
\(854\) | 11210.1 | 0.449183 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35959.1 | −1.43581 | ||||||||
\(857\) | −17226.4 | −0.686629 | −0.343314 | − | 0.939221i | \(-0.611550\pi\) | ||||
−0.343314 | + | 0.939221i | \(0.611550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33392.3 | −1.32634 | −0.663172 | − | 0.748467i | \(-0.730790\pi\) | ||||
−0.663172 | + | 0.748467i | \(0.730790\pi\) | |||||||
\(860\) | 11619.8 | 0.460735 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3713.11 | 0.146716 | ||||||||
\(863\) | 17381.9 | 0.685614 | 0.342807 | − | 0.939406i | \(-0.388622\pi\) | ||||
0.342807 | + | 0.939406i | \(0.388622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30697.9 | −1.20666 | ||||||||
\(866\) | 17086.8 | 0.670476 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24919.3 | 0.974443 | ||||||||
\(869\) | 61717.2 | 2.40922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −26538.8 | −1.03064 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12821.2 | −0.496207 | ||||||||
\(875\) | 33850.5 | 1.30783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14335.6 | 0.551970 | 0.275985 | − | 0.961162i | \(-0.410996\pi\) | ||||
0.275985 | + | 0.961162i | \(0.410996\pi\) | |||||||
\(878\) | −2796.02 | −0.107473 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6646.06 | −0.254589 | ||||||||
\(881\) | −5436.53 | −0.207901 | −0.103951 | − | 0.994582i | \(-0.533148\pi\) | ||||
−0.103951 | + | 0.994582i | \(0.533148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21185.9 | 0.807430 | 0.403715 | − | 0.914885i | \(-0.367719\pi\) | ||||
0.403715 | + | 0.914885i | \(0.367719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17688.6 | −0.670724 | ||||||||
\(887\) | 12661.4 | 0.479287 | 0.239644 | − | 0.970861i | \(-0.422969\pi\) | ||||
0.239644 | + | 0.970861i | \(0.422969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26255.5 | 0.990531 | ||||||||
\(890\) | 7767.94 | 0.292564 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19669.0 | 0.738305 | ||||||||
\(893\) | −7895.63 | −0.295876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26475.3 | 0.988794 | ||||||||
\(896\) | −27549.1 | −1.02718 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21462.3 | 0.797558 | ||||||||
\(899\) | 2775.54 | 0.102969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59145.8 | 2.18694 | ||||||||
\(902\) | 20365.9 | 0.751786 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23231.3 | 0.854715 | ||||||||
\(905\) | −37388.6 | −1.37330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3545.27 | 0.129789 | 0.0648946 | − | 0.997892i | \(-0.479329\pi\) | ||||
0.0648946 | + | 0.997892i | \(0.479329\pi\) | |||||||
\(908\) | 30263.1 | 1.10607 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3913.88 | 0.142341 | 0.0711706 | − | 0.997464i | \(-0.477327\pi\) | ||||
0.0711706 | + | 0.997464i | \(0.477327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25857.7 | 0.937313 | ||||||||
\(914\) | 3618.46 | 0.130950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27110.2 | −0.977890 | ||||||||
\(917\) | 32319.5 | 1.16389 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6917.79 | 0.248310 | 0.124155 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124155 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(920\) | −14492.5 | −0.519352 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9708.18 | 0.346770 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4897.57 | 0.174088 | ||||||||
\(926\) | −96.7050 | −0.00343188 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2653.15 | −0.0938512 | ||||||||
\(929\) | 3753.03 | 0.132543 | 0.0662717 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662717 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18367.1 | 0.646571 | ||||||||
\(932\) | −27336.4 | −0.960765 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11968.7 | 0.419302 | ||||||||
\(935\) | 41855.1 | 1.46397 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48189.0 | 1.68011 | 0.840056 | − | 0.542499i | \(-0.182522\pi\) | ||||
0.840056 | + | 0.542499i | \(0.182522\pi\) | |||||||
\(938\) | 26180.4 | 0.911323 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3705.17 | −0.128563 | ||||||||
\(941\) | −26656.4 | −0.923456 | −0.461728 | − | 0.887022i | \(-0.652770\pi\) | ||||
−0.461728 | + | 0.887022i | \(0.652770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19132.3 | −0.660693 | ||||||||
\(944\) | 1257.50 | 0.0433559 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16237.1 | 0.558047 | ||||||||
\(947\) | −31258.9 | −1.07263 | −0.536314 | − | 0.844018i | \(-0.680184\pi\) | ||||
−0.536314 | + | 0.844018i | \(0.680184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5647.60 | −0.192876 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 40150.0 | 1.36688 | ||||||||
\(953\) | −10602.4 | −0.360382 | −0.180191 | − | 0.983632i | \(-0.557672\pi\) | ||||
−0.180191 | + | 0.983632i | \(0.557672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8965.81 | −0.303798 | ||||||||
\(956\) | 9558.44 | 0.323370 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19856.9 | 0.669674 | ||||||||
\(959\) | −11378.6 | −0.383144 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8709.45 | 0.292352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3775.60 | 0.126145 | ||||||||
\(965\) | 21842.6 | 0.728640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4815.93 | −0.160155 | −0.0800774 | − | 0.996789i | \(-0.525517\pi\) | ||||
−0.0800774 | + | 0.996789i | \(0.525517\pi\) | |||||||
\(968\) | −25000.0 | −0.830092 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1092.97 | 0.0361786 | ||||||||
\(971\) | −56729.5 | −1.87491 | −0.937454 | − | 0.348109i | \(-0.886824\pi\) | ||||
−0.937454 | + | 0.348109i | \(0.886824\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16929.9 | −0.557808 | ||||||||
\(974\) | −106.493 | −0.00350334 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4500.40 | 0.147597 | ||||||||
\(977\) | 55246.2 | 1.80909 | 0.904546 | − | 0.426375i | \(-0.140210\pi\) | ||||
0.904546 | + | 0.426375i | \(0.140210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26555.4 | −0.866921 | ||||||||
\(980\) | 8619.11 | 0.280946 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4000.34 | 0.129996 | ||||||||
\(983\) | 22820.6 | 0.740451 | 0.370226 | − | 0.928942i | \(-0.379280\pi\) | ||||
0.370226 | + | 0.928942i | \(0.379280\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21882.0 | −0.707836 | ||||||||
\(986\) | 1856.54 | 0.0599637 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15253.5 | −0.490429 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46490.4 | −1.49023 | −0.745115 | − | 0.666936i | \(-0.767605\pi\) | ||||
−0.745115 | + | 0.666936i | \(0.767605\pi\) | |||||||
\(992\) | −36802.8 | −1.17791 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9028.21 | −0.288086 | ||||||||
\(995\) | 2519.84 | 0.0802856 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24943.4 | 0.792344 | 0.396172 | − | 0.918176i | \(-0.370338\pi\) | ||||
0.396172 | + | 0.918176i | \(0.370338\pi\) | |||||||
\(998\) | 11626.8 | 0.368777 | ||||||||
\(999\) | 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 | 1521.4.a.w.1.3 | 4 | ||
3.2 | odd | 2 | 507.4.a.l.1.2 | 4 | |||
13.5 | odd | 4 | 117.4.b.e.64.2 | 4 | |||
13.8 | odd | 4 | 117.4.b.e.64.3 | 4 | |||
13.12 | even | 2 | inner | 1521.4.a.w.1.2 | 4 | ||
39.5 | even | 4 | 39.4.b.b.25.3 | yes | 4 | ||
39.8 | even | 4 | 39.4.b.b.25.2 | ✓ | 4 | ||
39.38 | odd | 2 | 507.4.a.l.1.3 | 4 | |||
156.47 | odd | 4 | 624.4.c.c.337.3 | 4 | |||
156.83 | odd | 4 | 624.4.c.c.337.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.2 | ✓ | 4 | 39.8 | even | 4 | ||
39.4.b.b.25.3 | yes | 4 | 39.5 | even | 4 | ||
117.4.b.e.64.2 | 4 | 13.5 | odd | 4 | |||
117.4.b.e.64.3 | 4 | 13.8 | odd | 4 | |||
507.4.a.l.1.2 | 4 | 3.2 | odd | 2 | |||
507.4.a.l.1.3 | 4 | 39.38 | odd | 2 | |||
624.4.c.c.337.2 | 4 | 156.83 | odd | 4 | |||
624.4.c.c.337.3 | 4 | 156.47 | odd | 4 | |||
1521.4.a.w.1.2 | 4 | 13.12 | even | 2 | inner | ||
1521.4.a.w.1.3 | 4 | 1.1 | even | 1 | trivial |