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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 25x^{2} + 24x + 78 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
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 | 1.2 | ||
Root | \(-1.46610\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46610 | −0.518345 | −0.259173 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259173 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.85055 | −0.731318 | ||||||||
\(5\) | 9.85055 | 0.881060 | 0.440530 | − | 0.897738i | \(-0.354791\pi\) | ||||
0.440530 | + | 0.897738i | \(0.354791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.9396 | −1.61659 | −0.808293 | − | 0.588780i | \(-0.799608\pi\) | ||||
−0.808293 | + | 0.588780i | \(0.799608\pi\) | |||||||
\(8\) | 20.3063 | 0.897421 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.4419 | −0.456693 | ||||||||
\(11\) | 46.9257 | 1.28624 | 0.643120 | − | 0.765765i | \(-0.277640\pi\) | ||||
0.643120 | + | 0.765765i | \(0.277640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 43.8945 | 0.837950 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.0333 | 0.266145 | ||||||||
\(17\) | 48.2616 | 0.688539 | 0.344270 | − | 0.938871i | \(-0.388127\pi\) | ||||
0.344270 | + | 0.938871i | \(0.388127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −120.300 | −1.45257 | −0.726283 | − | 0.687396i | \(-0.758754\pi\) | ||||
−0.726283 | + | 0.687396i | \(0.758754\pi\) | |||||||
\(20\) | −57.6311 | −0.644335 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −68.7979 | −0.666717 | ||||||||
\(23\) | −130.697 | −1.18488 | −0.592440 | − | 0.805615i | \(-0.701835\pi\) | ||||
−0.592440 | + | 0.805615i | \(0.701835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.9667 | −0.223734 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 175.163 | 1.18224 | ||||||||
\(29\) | 194.946 | 1.24829 | 0.624147 | − | 0.781307i | \(-0.285447\pi\) | ||||
0.624147 | + | 0.781307i | \(0.285447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.0123 | 0.185470 | 0.0927351 | − | 0.995691i | \(-0.470439\pi\) | ||||
0.0927351 | + | 0.995691i | \(0.470439\pi\) | |||||||
\(32\) | −187.423 | −1.03538 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −70.7565 | −0.356901 | ||||||||
\(35\) | −294.921 | −1.42431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.4250 | 0.144071 | 0.0720355 | − | 0.997402i | \(-0.477051\pi\) | ||||
0.0720355 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(38\) | 176.372 | 0.752931 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 200.028 | 0.790681 | ||||||||
\(41\) | −241.825 | −0.921140 | −0.460570 | − | 0.887623i | \(-0.652355\pi\) | ||||
−0.460570 | + | 0.887623i | \(0.652355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96.4087 | 0.341911 | 0.170956 | − | 0.985279i | \(-0.445314\pi\) | ||||
0.170956 | + | 0.985279i | \(0.445314\pi\) | |||||||
\(44\) | −274.541 | −0.940651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 191.615 | 0.614177 | ||||||||
\(47\) | 539.015 | 1.67284 | 0.836419 | − | 0.548090i | \(-0.184645\pi\) | ||||
0.836419 | + | 0.548090i | \(0.184645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 553.380 | 1.61335 | ||||||||
\(50\) | 41.0021 | 0.115971 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 152.277 | 0.394657 | 0.197328 | − | 0.980337i | \(-0.436774\pi\) | ||||
0.197328 | + | 0.980337i | \(0.436774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 462.244 | 1.13325 | ||||||||
\(56\) | −607.963 | −1.45076 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −285.810 | −0.647047 | ||||||||
\(59\) | 327.792 | 0.723304 | 0.361652 | − | 0.932313i | \(-0.382213\pi\) | ||||
0.361652 | + | 0.932313i | \(0.382213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −98.4180 | −0.206576 | −0.103288 | − | 0.994651i | \(-0.532936\pi\) | ||||
−0.103288 | + | 0.994651i | \(0.532936\pi\) | |||||||
\(62\) | −46.9332 | −0.0961376 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 138.515 | 0.270537 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 441.151 | 0.804405 | 0.402202 | − | 0.915551i | \(-0.368245\pi\) | ||||
0.402202 | + | 0.915551i | \(0.368245\pi\) | |||||||
\(68\) | −282.357 | −0.503541 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 432.385 | 0.738284 | ||||||||
\(71\) | 345.049 | 0.576757 | 0.288379 | − | 0.957516i | \(-0.406884\pi\) | ||||
0.288379 | + | 0.957516i | \(0.406884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −773.839 | −1.24070 | −0.620349 | − | 0.784326i | \(-0.713009\pi\) | ||||
−0.620349 | + | 0.784326i | \(0.713009\pi\) | |||||||
\(74\) | −47.5383 | −0.0746785 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 703.822 | 1.06229 | ||||||||
\(77\) | −1404.94 | −2.07932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −150.332 | −0.214097 | −0.107049 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107049 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(80\) | 167.787 | 0.234489 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 354.540 | 0.477469 | ||||||||
\(83\) | 337.966 | 0.446947 | 0.223473 | − | 0.974710i | \(-0.428260\pi\) | ||||
0.223473 | + | 0.974710i | \(0.428260\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 475.403 | 0.606644 | ||||||||
\(86\) | −141.345 | −0.177228 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 952.889 | 1.15430 | ||||||||
\(89\) | 169.913 | 0.202368 | 0.101184 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101184 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 764.649 | 0.866524 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −790.250 | −0.867108 | ||||||||
\(95\) | −1185.02 | −1.27980 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −214.201 | −0.224215 | −0.112107 | − | 0.993696i | \(-0.535760\pi\) | ||||
−0.112107 | + | 0.993696i | \(0.535760\pi\) | |||||||
\(98\) | −811.311 | −0.836273 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 163.621 | 0.163621 | ||||||||
\(101\) | −1595.11 | −1.57148 | −0.785741 | − | 0.618556i | \(-0.787718\pi\) | ||||
−0.785741 | + | 0.618556i | \(0.787718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1570.30 | −1.50219 | −0.751096 | − | 0.660193i | \(-0.770475\pi\) | ||||
−0.751096 | + | 0.660193i | \(0.770475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −223.253 | −0.204568 | ||||||||
\(107\) | 6.73302 | 0.00608323 | 0.00304161 | − | 0.999995i | \(-0.499032\pi\) | ||||
0.00304161 | + | 0.999995i | \(0.499032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 542.422 | 0.476648 | 0.238324 | − | 0.971186i | \(-0.423402\pi\) | ||||
0.238324 | + | 0.971186i | \(0.423402\pi\) | |||||||
\(110\) | −677.697 | −0.587417 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −509.969 | −0.430246 | ||||||||
\(113\) | 1442.82 | 1.20114 | 0.600572 | − | 0.799571i | \(-0.294940\pi\) | ||||
0.600572 | + | 0.799571i | \(0.294940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1287.44 | −1.04395 | ||||||||
\(116\) | −1140.54 | −0.912900 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −480.577 | −0.374921 | ||||||||
\(119\) | −1444.93 | −1.11308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 871.025 | 0.654414 | ||||||||
\(122\) | 144.291 | 0.107078 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −187.289 | −0.135638 | ||||||||
\(125\) | −1506.81 | −1.07818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2492.84 | −1.74176 | −0.870881 | − | 0.491494i | \(-0.836451\pi\) | ||||
−0.870881 | + | 0.491494i | \(0.836451\pi\) | |||||||
\(128\) | 1296.31 | 0.895144 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −744.561 | −0.496585 | −0.248292 | − | 0.968685i | \(-0.579869\pi\) | ||||
−0.248292 | + | 0.968685i | \(0.579869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3601.74 | 2.34820 | ||||||||
\(134\) | −646.772 | −0.416959 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 980.016 | 0.617909 | ||||||||
\(137\) | −222.167 | −0.138547 | −0.0692736 | − | 0.997598i | \(-0.522068\pi\) | ||||
−0.0692736 | + | 0.997598i | \(0.522068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −777.145 | −0.474220 | −0.237110 | − | 0.971483i | \(-0.576200\pi\) | ||||
−0.237110 | + | 0.971483i | \(0.576200\pi\) | |||||||
\(140\) | 1725.45 | 1.04162 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −505.876 | −0.298959 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1920.32 | 1.09982 | ||||||||
\(146\) | 1134.53 | 0.643110 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −189.704 | −0.105362 | ||||||||
\(149\) | 1778.29 | 0.977742 | 0.488871 | − | 0.872356i | \(-0.337409\pi\) | ||||
0.488871 | + | 0.872356i | \(0.337409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1166.00 | −0.628394 | −0.314197 | − | 0.949358i | \(-0.601735\pi\) | ||||
−0.314197 | + | 0.949358i | \(0.601735\pi\) | |||||||
\(152\) | −2442.85 | −1.30356 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2059.78 | 1.07780 | ||||||||
\(155\) | 315.338 | 0.163410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 517.628 | 0.263129 | 0.131564 | − | 0.991308i | \(-0.458000\pi\) | ||||
0.131564 | + | 0.991308i | \(0.458000\pi\) | |||||||
\(158\) | 220.402 | 0.110976 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1846.22 | −0.912227 | ||||||||
\(161\) | 3913.02 | 1.91546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −610.188 | −0.293212 | −0.146606 | − | 0.989195i | \(-0.546835\pi\) | ||||
−0.146606 | + | 0.989195i | \(0.546835\pi\) | |||||||
\(164\) | 1414.81 | 0.673647 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −495.493 | −0.231673 | ||||||||
\(167\) | 2983.01 | 1.38223 | 0.691115 | − | 0.722745i | \(-0.257120\pi\) | ||||
0.691115 | + | 0.722745i | \(0.257120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −696.990 | −0.314451 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −564.044 | −0.250046 | ||||||||
\(173\) | −978.212 | −0.429896 | −0.214948 | − | 0.976625i | \(-0.568958\pi\) | ||||
−0.214948 | + | 0.976625i | \(0.568958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 837.313 | 0.361685 | ||||||||
\(176\) | 799.298 | 0.342326 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −249.110 | −0.104897 | ||||||||
\(179\) | −1852.94 | −0.773717 | −0.386858 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386858 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 852.777 | 0.350201 | 0.175101 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2653.98 | −1.06334 | ||||||||
\(185\) | 319.403 | 0.126935 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2264.71 | 0.885627 | ||||||||
\(188\) | −3153.53 | −1.22338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1737.36 | 0.663377 | ||||||||
\(191\) | −4441.29 | −1.68252 | −0.841258 | − | 0.540633i | \(-0.818185\pi\) | ||||
−0.841258 | + | 0.540633i | \(0.818185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2482.43 | 0.925851 | 0.462925 | − | 0.886397i | \(-0.346800\pi\) | ||||
0.462925 | + | 0.886397i | \(0.346800\pi\) | |||||||
\(194\) | 314.041 | 0.116221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3237.57 | −1.17987 | ||||||||
\(197\) | 1260.23 | 0.455775 | 0.227888 | − | 0.973687i | \(-0.426818\pi\) | ||||
0.227888 | + | 0.973687i | \(0.426818\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5520.96 | −1.96669 | −0.983344 | − | 0.181756i | \(-0.941822\pi\) | ||||
−0.983344 | + | 0.181756i | \(0.941822\pi\) | |||||||
\(200\) | −567.901 | −0.200783 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2338.60 | 0.814570 | ||||||||
\(203\) | −5836.60 | −2.01798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2382.11 | −0.811580 | ||||||||
\(206\) | 2302.21 | 0.778654 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5645.18 | −1.86835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4527.79 | −1.47728 | −0.738640 | − | 0.674100i | \(-0.764532\pi\) | ||||
−0.738640 | + | 0.674100i | \(0.764532\pi\) | |||||||
\(212\) | −890.901 | −0.288620 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.87129 | −0.00315321 | ||||||||
\(215\) | 949.679 | 0.301244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −958.435 | −0.299829 | ||||||||
\(218\) | −795.245 | −0.247068 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2704.38 | −0.828770 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4481.17 | −1.34566 | −0.672829 | − | 0.739798i | \(-0.734921\pi\) | ||||
−0.672829 | + | 0.739798i | \(0.734921\pi\) | |||||||
\(224\) | 5611.37 | 1.67377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2115.32 | −0.622607 | ||||||||
\(227\) | −5759.75 | −1.68409 | −0.842044 | − | 0.539408i | \(-0.818648\pi\) | ||||
−0.842044 | + | 0.539408i | \(0.818648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4635.08 | 1.33753 | 0.668766 | − | 0.743473i | \(-0.266823\pi\) | ||||
0.668766 | + | 0.743473i | \(0.266823\pi\) | |||||||
\(230\) | 1887.51 | 0.541126 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3958.63 | 1.12024 | ||||||||
\(233\) | −5886.33 | −1.65505 | −0.827524 | − | 0.561431i | \(-0.810251\pi\) | ||||
−0.827524 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5309.59 | 1.47387 | ||||||||
\(236\) | −1917.76 | −0.528965 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2118.42 | 0.576961 | ||||||||
\(239\) | 2135.84 | 0.578060 | 0.289030 | − | 0.957320i | \(-0.406667\pi\) | ||||
0.289030 | + | 0.957320i | \(0.406667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4692.92 | −1.25435 | −0.627173 | − | 0.778880i | \(-0.715788\pi\) | ||||
−0.627173 | + | 0.778880i | \(0.715788\pi\) | |||||||
\(242\) | −1277.01 | −0.339212 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 575.799 | 0.151073 | ||||||||
\(245\) | 5451.09 | 1.42146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 650.051 | 0.166445 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2209.13 | 0.558871 | ||||||||
\(251\) | 3902.88 | 0.981464 | 0.490732 | − | 0.871310i | \(-0.336729\pi\) | ||||
0.490732 | + | 0.871310i | \(0.336729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6133.06 | −1.52404 | ||||||||
\(254\) | 3654.76 | 0.902834 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3008.64 | −0.734531 | ||||||||
\(257\) | 4130.83 | 1.00262 | 0.501312 | − | 0.865267i | \(-0.332851\pi\) | ||||
0.501312 | + | 0.865267i | \(0.332851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −970.790 | −0.232903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1091.60 | 0.257402 | ||||||||
\(263\) | −6352.17 | −1.48932 | −0.744661 | − | 0.667443i | \(-0.767389\pi\) | ||||
−0.744661 | + | 0.667443i | \(0.767389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1500.01 | 0.347716 | ||||||||
\(266\) | −5280.52 | −1.21718 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2580.97 | −0.588276 | ||||||||
\(269\) | −181.524 | −0.0411439 | −0.0205719 | − | 0.999788i | \(-0.506549\pi\) | ||||
−0.0205719 | + | 0.999788i | \(0.506549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3460.35 | −0.775651 | −0.387825 | − | 0.921733i | \(-0.626774\pi\) | ||||
−0.387825 | + | 0.921733i | \(0.626774\pi\) | |||||||
\(272\) | 822.053 | 0.183251 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 325.719 | 0.0718153 | ||||||||
\(275\) | −1312.36 | −0.287776 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6437.94 | −1.39646 | −0.698228 | − | 0.715876i | \(-0.746028\pi\) | ||||
−0.698228 | + | 0.715876i | \(0.746028\pi\) | |||||||
\(278\) | 1139.37 | 0.245810 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5988.77 | −1.27820 | ||||||||
\(281\) | −2974.26 | −0.631421 | −0.315711 | − | 0.948855i | \(-0.602243\pi\) | ||||
−0.315711 | + | 0.948855i | \(0.602243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3035.72 | 0.637649 | 0.318825 | − | 0.947814i | \(-0.396712\pi\) | ||||
0.318825 | + | 0.947814i | \(0.396712\pi\) | |||||||
\(284\) | −2018.72 | −0.421793 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7240.15 | 1.48910 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2583.81 | −0.525914 | ||||||||
\(290\) | −2815.39 | −0.570087 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4527.38 | 0.907346 | ||||||||
\(293\) | −1955.74 | −0.389952 | −0.194976 | − | 0.980808i | \(-0.562463\pi\) | ||||
−0.194976 | + | 0.980808i | \(0.562463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3228.93 | 0.637274 | ||||||||
\(296\) | 658.431 | 0.129292 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2607.16 | −0.506808 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2886.44 | −0.552729 | ||||||||
\(302\) | 1709.47 | 0.325725 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2049.10 | −0.386593 | ||||||||
\(305\) | −969.471 | −0.182006 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1027.56 | 0.191029 | 0.0955147 | − | 0.995428i | \(-0.469550\pi\) | ||||
0.0955147 | + | 0.995428i | \(0.469550\pi\) | |||||||
\(308\) | 8219.66 | 1.52064 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −462.318 | −0.0847029 | ||||||||
\(311\) | −3405.61 | −0.620947 | −0.310474 | − | 0.950582i | \(-0.600488\pi\) | ||||
−0.310474 | + | 0.950582i | \(0.600488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4813.20 | 0.869196 | 0.434598 | − | 0.900625i | \(-0.356890\pi\) | ||||
0.434598 | + | 0.900625i | \(0.356890\pi\) | |||||||
\(314\) | −758.895 | −0.136391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 879.525 | 0.156573 | ||||||||
\(317\) | 1141.33 | 0.202219 | 0.101110 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101110 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9147.98 | 1.60561 | ||||||||
\(320\) | 1364.45 | 0.238359 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5736.88 | −0.992870 | ||||||||
\(323\) | −5805.88 | −1.00015 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 894.597 | 0.151985 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4910.58 | −0.826650 | ||||||||
\(329\) | −16137.9 | −2.70429 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7652.57 | −1.27076 | −0.635382 | − | 0.772198i | \(-0.719157\pi\) | ||||
−0.635382 | + | 0.772198i | \(0.719157\pi\) | |||||||
\(332\) | −1977.29 | −0.326860 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4373.40 | −0.716472 | ||||||||
\(335\) | 4345.57 | 0.708729 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2503.69 | −0.404702 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2781.37 | −0.443650 | ||||||||
\(341\) | 1502.20 | 0.238559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6298.69 | −0.991537 | ||||||||
\(344\) | 1957.71 | 0.306838 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1434.16 | 0.222835 | ||||||||
\(347\) | −4496.12 | −0.695574 | −0.347787 | − | 0.937574i | \(-0.613067\pi\) | ||||
−0.347787 | + | 0.937574i | \(0.613067\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3577.61 | −0.548726 | −0.274363 | − | 0.961626i | \(-0.588467\pi\) | ||||
−0.274363 | + | 0.961626i | \(0.588467\pi\) | |||||||
\(350\) | −1227.59 | −0.187478 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8794.96 | −1.33174 | ||||||||
\(353\) | −8045.17 | −1.21303 | −0.606517 | − | 0.795070i | \(-0.707434\pi\) | ||||
−0.606517 | + | 0.795070i | \(0.707434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3398.92 | 0.508157 | ||||||||
\(356\) | −994.086 | −0.147996 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2716.60 | 0.401052 | ||||||||
\(359\) | −2172.90 | −0.319447 | −0.159724 | − | 0.987162i | \(-0.551060\pi\) | ||||
−0.159724 | + | 0.987162i | \(0.551060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7613.14 | 1.10995 | ||||||||
\(362\) | −1250.26 | −0.181525 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7622.74 | −1.09313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7662.76 | 1.08990 | 0.544949 | − | 0.838469i | \(-0.316549\pi\) | ||||
0.544949 | + | 0.838469i | \(0.316549\pi\) | |||||||
\(368\) | −2226.20 | −0.315349 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −468.278 | −0.0657962 | ||||||||
\(371\) | −4559.10 | −0.637996 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10542.5 | 1.46346 | 0.731732 | − | 0.681593i | \(-0.238712\pi\) | ||||
0.731732 | + | 0.681593i | \(0.238712\pi\) | |||||||
\(374\) | −3320.30 | −0.459060 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10945.4 | 1.50124 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5475.54 | −0.742110 | −0.371055 | − | 0.928611i | \(-0.621004\pi\) | ||||
−0.371055 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(380\) | 6933.03 | 0.935939 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6511.39 | 0.872124 | ||||||||
\(383\) | 808.085 | 0.107810 | 0.0539050 | − | 0.998546i | \(-0.482833\pi\) | ||||
0.0539050 | + | 0.998546i | \(0.482833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13839.4 | −1.83200 | ||||||||
\(386\) | −3639.49 | −0.479910 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1253.19 | 0.163972 | ||||||||
\(389\) | 7060.26 | 0.920230 | 0.460115 | − | 0.887859i | \(-0.347808\pi\) | ||||
0.460115 | + | 0.887859i | \(0.347808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6307.65 | −0.815836 | ||||||||
\(392\) | 11237.1 | 1.44786 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1847.63 | −0.236249 | ||||||||
\(395\) | −1480.85 | −0.188633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1419.89 | 0.179502 | 0.0897511 | − | 0.995964i | \(-0.471393\pi\) | ||||
0.0897511 | + | 0.995964i | \(0.471393\pi\) | |||||||
\(398\) | 8094.29 | 1.01942 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −476.365 | −0.0595456 | ||||||||
\(401\) | 10670.7 | 1.32886 | 0.664428 | − | 0.747353i | \(-0.268675\pi\) | ||||
0.664428 | + | 0.747353i | \(0.268675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9332.28 | 1.14925 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8557.05 | 1.04601 | ||||||||
\(407\) | 1521.56 | 0.185310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6351.56 | −0.767883 | −0.383942 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383942 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(410\) | 3492.42 | 0.420678 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9187.09 | 1.09858 | ||||||||
\(413\) | −9813.97 | −1.16928 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3329.15 | 0.393787 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8276.40 | 0.968450 | ||||||||
\(419\) | −5617.87 | −0.655015 | −0.327507 | − | 0.944849i | \(-0.606209\pi\) | ||||
−0.327507 | + | 0.944849i | \(0.606209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1518.29 | 0.175765 | 0.0878825 | − | 0.996131i | \(-0.471990\pi\) | ||||
0.0878825 | + | 0.996131i | \(0.471990\pi\) | |||||||
\(422\) | 6638.20 | 0.765741 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3092.17 | 0.354173 | ||||||||
\(425\) | −1349.72 | −0.154050 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2946.60 | 0.333948 | ||||||||
\(428\) | −39.3918 | −0.00444878 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1392.33 | −0.156149 | ||||||||
\(431\) | −4970.13 | −0.555459 | −0.277730 | − | 0.960659i | \(-0.589582\pi\) | ||||
−0.277730 | + | 0.960659i | \(0.589582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3298.71 | −0.366111 | −0.183055 | − | 0.983103i | \(-0.558599\pi\) | ||||
−0.183055 | + | 0.983103i | \(0.558599\pi\) | |||||||
\(434\) | 1405.16 | 0.155415 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3173.46 | −0.348581 | ||||||||
\(437\) | 15722.9 | 1.72112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6048.47 | −0.657581 | −0.328790 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328790 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(440\) | 9386.47 | 1.01701 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6822.62 | −0.731722 | −0.365861 | − | 0.930670i | \(-0.619225\pi\) | ||||
−0.365861 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1673.74 | 0.178299 | ||||||||
\(446\) | 6569.86 | 0.697515 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4147.09 | −0.437347 | ||||||||
\(449\) | 410.410 | 0.0431369 | 0.0215684 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215684 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11347.8 | −1.18481 | ||||||||
\(452\) | −8441.30 | −0.878419 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8444.38 | 0.872939 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16642.8 | 1.70354 | 0.851771 | − | 0.523915i | \(-0.175529\pi\) | ||||
0.851771 | + | 0.523915i | \(0.175529\pi\) | |||||||
\(458\) | −6795.50 | −0.693303 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7532.21 | 0.763459 | ||||||||
\(461\) | −11729.7 | −1.18505 | −0.592523 | − | 0.805553i | \(-0.701868\pi\) | ||||
−0.592523 | + | 0.805553i | \(0.701868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3564.93 | 0.357832 | 0.178916 | − | 0.983864i | \(-0.442741\pi\) | ||||
0.178916 | + | 0.983864i | \(0.442741\pi\) | |||||||
\(464\) | 3320.56 | 0.332227 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8629.95 | 0.857886 | ||||||||
\(467\) | −1134.81 | −0.112447 | −0.0562233 | − | 0.998418i | \(-0.517906\pi\) | ||||
−0.0562233 | + | 0.998418i | \(0.517906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13207.9 | −1.30039 | ||||||||
\(470\) | −7784.40 | −0.763974 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6656.25 | 0.649107 | ||||||||
\(473\) | 4524.05 | 0.439780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3364.40 | 0.324988 | ||||||||
\(476\) | 8453.65 | 0.814018 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3131.36 | −0.299635 | ||||||||
\(479\) | −19372.6 | −1.84793 | −0.923963 | − | 0.382481i | \(-0.875070\pi\) | ||||
−0.923963 | + | 0.382481i | \(0.875070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6880.29 | 0.650184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5095.97 | −0.478585 | ||||||||
\(485\) | −2110.00 | −0.197547 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9045.95 | 0.841707 | 0.420853 | − | 0.907129i | \(-0.361731\pi\) | ||||
0.420853 | + | 0.907129i | \(0.361731\pi\) | |||||||
\(488\) | −1998.51 | −0.185385 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7991.86 | −0.736807 | ||||||||
\(491\) | −14403.3 | −1.32385 | −0.661927 | − | 0.749568i | \(-0.730261\pi\) | ||||
−0.661927 | + | 0.749568i | \(0.730261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9408.40 | 0.859499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 545.273 | 0.0493619 | ||||||||
\(497\) | −10330.6 | −0.932378 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9319.75 | 0.836091 | 0.418045 | − | 0.908426i | \(-0.362715\pi\) | ||||
0.418045 | + | 0.908426i | \(0.362715\pi\) | |||||||
\(500\) | 8815.64 | 0.788495 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5722.02 | −0.508737 | ||||||||
\(503\) | −2745.98 | −0.243414 | −0.121707 | − | 0.992566i | \(-0.538837\pi\) | ||||
−0.121707 | + | 0.992566i | \(0.538837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15712.7 | −1.38457 | ||||||||
\(506\) | 8991.69 | 0.789979 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14584.5 | 1.27378 | ||||||||
\(509\) | −1182.11 | −0.102939 | −0.0514697 | − | 0.998675i | \(-0.516391\pi\) | ||||
−0.0514697 | + | 0.998675i | \(0.516391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23168.4 | 2.00570 | ||||||||
\(512\) | −5959.48 | −0.514403 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6056.22 | −0.519705 | ||||||||
\(515\) | −15468.3 | −1.32352 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25293.7 | 2.15167 | ||||||||
\(518\) | 1423.28 | 0.120724 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10858.8 | −0.913115 | −0.456558 | − | 0.889694i | \(-0.650918\pi\) | ||||
−0.456558 | + | 0.889694i | \(0.650918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10161.7 | −0.849602 | −0.424801 | − | 0.905287i | \(-0.639656\pi\) | ||||
−0.424801 | + | 0.905287i | \(0.639656\pi\) | |||||||
\(524\) | 4356.09 | 0.363162 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9312.93 | 0.771983 | ||||||||
\(527\) | 1544.96 | 0.127703 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4914.73 | 0.403939 | ||||||||
\(530\) | −2199.16 | −0.180237 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21072.1 | −1.71728 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66.3239 | 0.00535969 | ||||||||
\(536\) | 8958.14 | 0.721889 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 266.132 | 0.0213267 | ||||||||
\(539\) | 25967.8 | 2.07516 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9573.04 | 0.760771 | 0.380386 | − | 0.924828i | \(-0.375791\pi\) | ||||
0.380386 | + | 0.924828i | \(0.375791\pi\) | |||||||
\(542\) | 5073.23 | 0.402055 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9045.34 | −0.712896 | ||||||||
\(545\) | 5343.15 | 0.419955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15958.9 | 1.24745 | 0.623724 | − | 0.781645i | \(-0.285619\pi\) | ||||
0.623724 | + | 0.781645i | \(0.285619\pi\) | |||||||
\(548\) | 1299.80 | 0.101322 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1924.05 | 0.149167 | ||||||||
\(551\) | −23452.0 | −1.81323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4500.89 | 0.346107 | ||||||||
\(554\) | 9438.67 | 0.723846 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4546.72 | 0.346806 | ||||||||
\(557\) | −2145.09 | −0.163178 | −0.0815892 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815892 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5023.47 | −0.379072 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4360.57 | 0.327294 | ||||||||
\(563\) | 22318.6 | 1.67072 | 0.835362 | − | 0.549701i | \(-0.185258\pi\) | ||||
0.835362 | + | 0.549701i | \(0.185258\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14212.6 | 1.05828 | ||||||||
\(566\) | −4450.67 | −0.330523 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7006.67 | 0.517594 | ||||||||
\(569\) | 19753.0 | 1.45534 | 0.727671 | − | 0.685927i | \(-0.240603\pi\) | ||||
0.727671 | + | 0.685927i | \(0.240603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10640.6 | −0.779850 | −0.389925 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389925 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10614.8 | −0.771870 | ||||||||
\(575\) | 3655.17 | 0.265098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6547.89 | −0.472430 | −0.236215 | − | 0.971701i | \(-0.575907\pi\) | ||||
−0.236215 | + | 0.971701i | \(0.575907\pi\) | |||||||
\(578\) | 3788.13 | 0.272605 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11234.9 | −0.804319 | ||||||||
\(581\) | −10118.6 | −0.722529 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7145.69 | 0.507623 | ||||||||
\(584\) | −15713.8 | −1.11343 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2867.32 | 0.202130 | ||||||||
\(587\) | 5900.33 | 0.414877 | 0.207439 | − | 0.978248i | \(-0.433487\pi\) | ||||
0.207439 | + | 0.978248i | \(0.433487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3851.08 | −0.269408 | ||||||||
\(590\) | −4733.94 | −0.330328 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 552.303 | 0.0383437 | ||||||||
\(593\) | −15261.5 | −1.05686 | −0.528428 | − | 0.848978i | \(-0.677218\pi\) | ||||
−0.528428 | + | 0.848978i | \(0.677218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14233.4 | −0.980693 | ||||||||
\(596\) | −10404.0 | −0.715041 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18900.6 | 1.28925 | 0.644623 | − | 0.764501i | \(-0.277014\pi\) | ||||
0.644623 | + | 0.764501i | \(0.277014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18507.0 | −1.25610 | −0.628049 | − | 0.778174i | \(-0.716146\pi\) | ||||
−0.628049 | + | 0.778174i | \(0.716146\pi\) | |||||||
\(602\) | 4231.81 | 0.286505 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6821.72 | 0.459556 | ||||||||
\(605\) | 8580.08 | 0.576578 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6408.50 | −0.428522 | −0.214261 | − | 0.976776i | \(-0.568734\pi\) | ||||
−0.214261 | + | 0.976776i | \(0.568734\pi\) | |||||||
\(608\) | 22547.0 | 1.50395 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1421.34 | 0.0943418 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3507.26 | 0.231088 | 0.115544 | − | 0.993302i | \(-0.463139\pi\) | ||||
0.115544 | + | 0.993302i | \(0.463139\pi\) | |||||||
\(614\) | −1506.51 | −0.0990192 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28529.1 | −1.86602 | ||||||||
\(617\) | 14507.8 | 0.946614 | 0.473307 | − | 0.880897i | \(-0.343060\pi\) | ||||
0.473307 | + | 0.880897i | \(0.343060\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4750.85 | −0.308486 | −0.154243 | − | 0.988033i | \(-0.549294\pi\) | ||||
−0.154243 | + | 0.988033i | \(0.549294\pi\) | |||||||
\(620\) | −1844.90 | −0.119505 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4992.98 | 0.321865 | ||||||||
\(623\) | −5087.14 | −0.327146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11347.0 | −0.726209 | ||||||||
\(626\) | −7056.65 | −0.450544 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3028.40 | −0.192431 | ||||||||
\(629\) | 1564.88 | 0.0991986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4825.19 | −0.304418 | −0.152209 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152209 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(632\) | −3052.69 | −0.192135 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1673.30 | −0.104819 | ||||||||
\(635\) | −24555.8 | −1.53460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13411.9 | −0.832258 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12769.3 | 0.788675 | ||||||||
\(641\) | 5911.89 | 0.364284 | 0.182142 | − | 0.983272i | \(-0.441697\pi\) | ||||
0.182142 | + | 0.983272i | \(0.441697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23408.3 | −1.43567 | −0.717833 | − | 0.696216i | \(-0.754866\pi\) | ||||
−0.717833 | + | 0.696216i | \(0.754866\pi\) | |||||||
\(644\) | −22893.3 | −1.40081 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8512.02 | 0.518422 | ||||||||
\(647\) | 16398.7 | 0.996442 | 0.498221 | − | 0.867050i | \(-0.333987\pi\) | ||||
0.498221 | + | 0.867050i | \(0.333987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15381.9 | 0.930342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3569.93 | 0.214431 | ||||||||
\(653\) | −27529.6 | −1.64979 | −0.824897 | − | 0.565283i | \(-0.808767\pi\) | ||||
−0.824897 | + | 0.565283i | \(0.808767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7334.34 | −0.437521 | ||||||||
\(656\) | −4119.07 | −0.245157 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23659.8 | 1.40175 | ||||||||
\(659\) | 24179.7 | 1.42930 | 0.714650 | − | 0.699482i | \(-0.246586\pi\) | ||||
0.714650 | + | 0.699482i | \(0.246586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4525.04 | −0.266269 | −0.133134 | − | 0.991098i | \(-0.542504\pi\) | ||||
−0.133134 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(662\) | 11219.4 | 0.658695 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6862.84 | 0.401099 | ||||||||
\(665\) | 35479.1 | 2.06890 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25478.8 | −1.47908 | ||||||||
\(668\) | −17452.2 | −1.01085 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6371.05 | −0.367366 | ||||||||
\(671\) | −4618.34 | −0.265706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3287.18 | 0.188279 | 0.0941393 | − | 0.995559i | \(-0.469990\pi\) | ||||
0.0941393 | + | 0.995559i | \(0.469990\pi\) | |||||||
\(674\) | 3670.66 | 0.209775 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9724.21 | 0.552041 | 0.276020 | − | 0.961152i | \(-0.410984\pi\) | ||||
0.276020 | + | 0.961152i | \(0.410984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6413.10 | 0.362463 | ||||||||
\(680\) | 9653.69 | 0.544415 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2202.38 | −0.123656 | ||||||||
\(683\) | 14548.7 | 0.815065 | 0.407532 | − | 0.913191i | \(-0.366389\pi\) | ||||
0.407532 | + | 0.913191i | \(0.366389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2188.46 | −0.122068 | ||||||||
\(686\) | 9234.52 | 0.513959 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1642.15 | 0.0909979 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6728.96 | −0.370451 | −0.185226 | − | 0.982696i | \(-0.559302\pi\) | ||||
−0.185226 | + | 0.982696i | \(0.559302\pi\) | |||||||
\(692\) | 5723.07 | 0.314391 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6591.76 | 0.360548 | ||||||||
\(695\) | −7655.31 | −0.417816 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11670.9 | −0.634241 | ||||||||
\(698\) | 5245.15 | 0.284429 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4898.74 | −0.264507 | ||||||||
\(701\) | 29159.8 | 1.57111 | 0.785557 | − | 0.618789i | \(-0.212376\pi\) | ||||
0.785557 | + | 0.618789i | \(0.212376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3900.73 | −0.209273 | ||||||||
\(704\) | 6499.92 | 0.347976 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11795.0 | 0.628770 | ||||||||
\(707\) | 47757.0 | 2.54044 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20489.0 | 1.08531 | 0.542653 | − | 0.839957i | \(-0.317420\pi\) | ||||
0.542653 | + | 0.839957i | \(0.317420\pi\) | |||||||
\(710\) | −4983.16 | −0.263401 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3450.31 | 0.181609 | ||||||||
\(713\) | −4183.91 | −0.219760 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10840.7 | 0.565833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3185.70 | 0.165584 | ||||||||
\(719\) | 17990.1 | 0.933127 | 0.466563 | − | 0.884488i | \(-0.345492\pi\) | ||||
0.466563 | + | 0.884488i | \(0.345492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47014.0 | 2.42842 | ||||||||
\(722\) | −11161.6 | −0.575337 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4989.21 | −0.256108 | ||||||||
\(725\) | −5452.00 | −0.279286 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37652.7 | −1.92086 | −0.960428 | − | 0.278528i | \(-0.910153\pi\) | ||||
−0.960428 | + | 0.278528i | \(0.910153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11175.7 | 0.566618 | ||||||||
\(731\) | 4652.84 | 0.235419 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4524.26 | −0.227977 | −0.113989 | − | 0.993482i | \(-0.536363\pi\) | ||||
−0.113989 | + | 0.993482i | \(0.536363\pi\) | |||||||
\(734\) | −11234.4 | −0.564944 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24495.6 | 1.22679 | ||||||||
\(737\) | 20701.3 | 1.03466 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −818.302 | −0.0407331 | −0.0203665 | − | 0.999793i | \(-0.506483\pi\) | ||||
−0.0203665 | + | 0.999793i | \(0.506483\pi\) | |||||||
\(740\) | −1868.68 | −0.0928300 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6684.10 | 0.330702 | ||||||||
\(743\) | 39002.2 | 1.92578 | 0.962888 | − | 0.269901i | \(-0.0869911\pi\) | ||||
0.962888 | + | 0.269901i | \(0.0869911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17517.2 | 0.861449 | ||||||||
\(746\) | −15456.4 | −0.758579 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13249.8 | −0.647675 | ||||||||
\(749\) | −201.584 | −0.00983407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22377.7 | −1.08732 | −0.543658 | − | 0.839307i | \(-0.682961\pi\) | ||||
−0.543658 | + | 0.839307i | \(0.682961\pi\) | |||||||
\(752\) | 9181.18 | 0.445217 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11485.7 | −0.553653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34512.6 | −1.65704 | −0.828521 | − | 0.559958i | \(-0.810817\pi\) | ||||
−0.828521 | + | 0.559958i | \(0.810817\pi\) | |||||||
\(758\) | 8027.70 | 0.384669 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24063.4 | −1.14852 | ||||||||
\(761\) | 19975.6 | 0.951529 | 0.475764 | − | 0.879573i | \(-0.342172\pi\) | ||||
0.475764 | + | 0.879573i | \(0.342172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16239.9 | −0.770542 | ||||||||
\(764\) | 25984.0 | 1.23046 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1184.73 | −0.0558827 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33064.9 | 1.55052 | 0.775260 | − | 0.631642i | \(-0.217619\pi\) | ||||
0.775260 | + | 0.631642i | \(0.217619\pi\) | |||||||
\(770\) | 20290.0 | 0.949610 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14523.6 | −0.677091 | ||||||||
\(773\) | −18564.0 | −0.863779 | −0.431890 | − | 0.901927i | \(-0.642153\pi\) | ||||
−0.431890 | + | 0.901927i | \(0.642153\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −895.279 | −0.0414960 | ||||||||
\(776\) | −4349.64 | −0.201215 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10351.1 | −0.476997 | ||||||||
\(779\) | 29091.6 | 1.33802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16191.7 | 0.741848 | ||||||||
\(782\) | 9247.66 | 0.422885 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9425.86 | 0.429385 | ||||||||
\(785\) | 5098.91 | 0.231832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36436.8 | −1.65036 | −0.825179 | − | 0.564871i | \(-0.808926\pi\) | ||||
−0.825179 | + | 0.564871i | \(0.808926\pi\) | |||||||
\(788\) | −7373.04 | −0.333317 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2171.08 | 0.0977768 | ||||||||
\(791\) | −43197.5 | −1.94175 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2081.71 | −0.0930441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32300.7 | 1.43827 | ||||||||
\(797\) | −12365.6 | −0.549576 | −0.274788 | − | 0.961505i | \(-0.588608\pi\) | ||||
−0.274788 | + | 0.961505i | \(0.588608\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26013.7 | 1.15181 | ||||||||
\(800\) | 5241.61 | 0.231649 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15644.4 | −0.688806 | ||||||||
\(803\) | −36313.0 | −1.59584 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38545.4 | 1.68763 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −32390.9 | −1.41028 | ||||||||
\(809\) | 8093.75 | 0.351744 | 0.175872 | − | 0.984413i | \(-0.443726\pi\) | ||||
0.175872 | + | 0.984413i | \(0.443726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15984.7 | −0.692105 | −0.346052 | − | 0.938215i | \(-0.612478\pi\) | ||||
−0.346052 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(812\) | 34147.3 | 1.47578 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2230.77 | −0.0960546 | ||||||||
\(815\) | −6010.68 | −0.258337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11598.0 | −0.496649 | ||||||||
\(818\) | 9312.03 | 0.398029 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13936.6 | 0.593523 | ||||||||
\(821\) | −26861.9 | −1.14188 | −0.570942 | − | 0.820990i | \(-0.693422\pi\) | ||||
−0.570942 | + | 0.820990i | \(0.693422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5205.94 | −0.220495 | −0.110248 | − | 0.993904i | \(-0.535164\pi\) | ||||
−0.110248 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(824\) | −31886.9 | −1.34810 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14388.3 | 0.606092 | ||||||||
\(827\) | 46621.5 | 1.96032 | 0.980162 | − | 0.198200i | \(-0.0635095\pi\) | ||||
0.980162 | + | 0.198200i | \(0.0635095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41829.7 | −1.75248 | −0.876241 | − | 0.481874i | \(-0.839956\pi\) | ||||
−0.876241 | + | 0.481874i | \(0.839956\pi\) | |||||||
\(830\) | −4880.87 | −0.204118 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26707.0 | 1.11086 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29384.3 | 1.21783 | ||||||||
\(836\) | 33027.4 | 1.36636 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8236.37 | 0.339524 | ||||||||
\(839\) | 12685.1 | 0.521975 | 0.260988 | − | 0.965342i | \(-0.415952\pi\) | ||||
0.260988 | + | 0.965342i | \(0.415952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13614.9 | 0.558238 | ||||||||
\(842\) | −2225.97 | −0.0911069 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26490.1 | 1.08036 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26078.2 | −1.05792 | ||||||||
\(848\) | 2593.77 | 0.105036 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1978.83 | 0.0798509 | ||||||||
\(851\) | −4237.85 | −0.170707 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37493.3 | 1.50498 | 0.752488 | − | 0.658606i | \(-0.228854\pi\) | ||||
0.752488 | + | 0.658606i | \(0.228854\pi\) | |||||||
\(854\) | −4320.01 | −0.173100 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 136.723 | 0.00545921 | ||||||||
\(857\) | 11826.3 | 0.471386 | 0.235693 | − | 0.971828i | \(-0.424264\pi\) | ||||
0.235693 | + | 0.971828i | \(0.424264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36498.7 | −1.44973 | −0.724866 | − | 0.688890i | \(-0.758099\pi\) | ||||
−0.724866 | + | 0.688890i | \(0.758099\pi\) | |||||||
\(860\) | −5556.14 | −0.220306 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7286.72 | 0.287920 | ||||||||
\(863\) | 2292.79 | 0.0904372 | 0.0452186 | − | 0.998977i | \(-0.485602\pi\) | ||||
0.0452186 | + | 0.998977i | \(0.485602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9635.92 | −0.378764 | ||||||||
\(866\) | 4836.24 | 0.189772 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5607.37 | 0.219270 | ||||||||
\(869\) | −7054.45 | −0.275381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11014.6 | 0.427753 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −23051.3 | −0.892132 | ||||||||
\(875\) | 45113.2 | 1.74298 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20800.3 | 0.800885 | 0.400442 | − | 0.916322i | \(-0.368856\pi\) | ||||
0.400442 | + | 0.916322i | \(0.368856\pi\) | |||||||
\(878\) | 8867.68 | 0.340854 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7873.52 | 0.301610 | ||||||||
\(881\) | 19255.9 | 0.736377 | 0.368188 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368188 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1744.49 | 0.0664857 | 0.0332429 | − | 0.999447i | \(-0.489417\pi\) | ||||
0.0332429 | + | 0.999447i | \(0.489417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10002.7 | 0.379284 | ||||||||
\(887\) | −2970.70 | −0.112454 | −0.0562268 | − | 0.998418i | \(-0.517907\pi\) | ||||
−0.0562268 | + | 0.998418i | \(0.517907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 74634.6 | 2.81571 | ||||||||
\(890\) | −2453.87 | −0.0924202 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26217.3 | 0.984104 | ||||||||
\(893\) | −64843.6 | −2.42991 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18252.5 | −0.681691 | ||||||||
\(896\) | −38810.9 | −1.44708 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −601.703 | −0.0223598 | ||||||||
\(899\) | 6240.66 | 0.231521 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7349.12 | 0.271736 | ||||||||
\(902\) | 16637.1 | 0.614140 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29298.4 | 1.07793 | ||||||||
\(905\) | 8400.32 | 0.308548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33003.3 | 1.20822 | 0.604111 | − | 0.796900i | \(-0.293528\pi\) | ||||
0.604111 | + | 0.796900i | \(0.293528\pi\) | |||||||
\(908\) | 33697.7 | 1.23160 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14977.0 | −0.544686 | −0.272343 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272343 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15859.3 | 0.574881 | ||||||||
\(914\) | −24400.1 | −0.883022 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27117.7 | −0.978161 | ||||||||
\(917\) | 22291.9 | 0.802773 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11425.4 | 0.410107 | 0.205054 | − | 0.978751i | \(-0.434263\pi\) | ||||
0.205054 | + | 0.978751i | \(0.434263\pi\) | |||||||
\(920\) | −26143.1 | −0.936862 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17196.9 | 0.614263 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −906.820 | −0.0322336 | ||||||||
\(926\) | −5226.55 | −0.185481 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36537.3 | −1.29245 | ||||||||
\(929\) | 11954.2 | 0.422179 | 0.211090 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211090 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −66571.7 | −2.34350 | ||||||||
\(932\) | 34438.2 | 1.21037 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1663.74 | 0.0582861 | ||||||||
\(935\) | 22308.7 | 0.780290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42546.4 | 1.48338 | 0.741692 | − | 0.670740i | \(-0.234024\pi\) | ||||
0.741692 | + | 0.670740i | \(0.234024\pi\) | |||||||
\(938\) | 19364.1 | 0.674051 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31064.0 | −1.07787 | ||||||||
\(941\) | 20665.1 | 0.715903 | 0.357951 | − | 0.933740i | \(-0.383475\pi\) | ||||
0.357951 | + | 0.933740i | \(0.383475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31605.9 | 1.09144 | ||||||||
\(944\) | 5583.37 | 0.192503 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6632.72 | −0.227958 | ||||||||
\(947\) | −9493.73 | −0.325771 | −0.162885 | − | 0.986645i | \(-0.552080\pi\) | ||||
−0.162885 | + | 0.986645i | \(0.552080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4932.56 | −0.168456 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29341.3 | −0.998904 | ||||||||
\(953\) | −53334.1 | −1.81287 | −0.906433 | − | 0.422349i | \(-0.861206\pi\) | ||||
−0.906433 | + | 0.422349i | \(0.861206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43749.2 | −1.48240 | ||||||||
\(956\) | −12495.9 | −0.422746 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28402.2 | 0.957864 | ||||||||
\(959\) | 6651.58 | 0.223974 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28766.2 | −0.965601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27456.1 | 0.917326 | ||||||||
\(965\) | 24453.3 | 0.815730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42110.1 | 1.40038 | 0.700191 | − | 0.713956i | \(-0.253098\pi\) | ||||
0.700191 | + | 0.713956i | \(0.253098\pi\) | |||||||
\(968\) | 17687.3 | 0.587285 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3093.47 | 0.102397 | ||||||||
\(971\) | 13827.7 | 0.457006 | 0.228503 | − | 0.973543i | \(-0.426617\pi\) | ||||
0.228503 | + | 0.973543i | \(0.426617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23267.4 | 0.766618 | ||||||||
\(974\) | −13262.3 | −0.436295 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1676.38 | −0.0549791 | ||||||||
\(977\) | 1133.89 | 0.0371302 | 0.0185651 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185651 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7973.31 | 0.260294 | ||||||||
\(980\) | −31891.9 | −1.03954 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21116.7 | 0.686214 | ||||||||
\(983\) | 26250.2 | 0.851729 | 0.425865 | − | 0.904787i | \(-0.359970\pi\) | ||||
0.425865 | + | 0.904787i | \(0.359970\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12414.0 | 0.401565 | ||||||||
\(986\) | −13793.7 | −0.445517 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12600.3 | −0.405124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29360.4 | −0.941133 | −0.470566 | − | 0.882365i | \(-0.655950\pi\) | ||||
−0.470566 | + | 0.882365i | \(0.655950\pi\) | |||||||
\(992\) | −5999.84 | −0.192031 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15145.7 | 0.483293 | ||||||||
\(995\) | −54384.5 | −1.73277 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16835.9 | 0.534803 | 0.267401 | − | 0.963585i | \(-0.413835\pi\) | ||||
0.267401 | + | 0.963585i | \(0.413835\pi\) | |||||||
\(998\) | −13663.7 | −0.433384 | ||||||||
\(999\) | 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.bb.1.2 | 4 | ||
3.2 | odd | 2 | 507.4.a.i.1.3 | 4 | |||
13.4 | even | 6 | 117.4.g.e.55.2 | 8 | |||
13.10 | even | 6 | 117.4.g.e.100.2 | 8 | |||
13.12 | even | 2 | 1521.4.a.v.1.3 | 4 | |||
39.5 | even | 4 | 507.4.b.h.337.4 | 8 | |||
39.8 | even | 4 | 507.4.b.h.337.5 | 8 | |||
39.17 | odd | 6 | 39.4.e.c.16.3 | ✓ | 8 | ||
39.23 | odd | 6 | 39.4.e.c.22.3 | yes | 8 | ||
39.38 | odd | 2 | 507.4.a.m.1.2 | 4 | |||
156.23 | even | 6 | 624.4.q.i.529.4 | 8 | |||
156.95 | even | 6 | 624.4.q.i.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.3 | ✓ | 8 | 39.17 | odd | 6 | ||
39.4.e.c.22.3 | yes | 8 | 39.23 | odd | 6 | ||
117.4.g.e.55.2 | 8 | 13.4 | even | 6 | |||
117.4.g.e.100.2 | 8 | 13.10 | even | 6 | |||
507.4.a.i.1.3 | 4 | 3.2 | odd | 2 | |||
507.4.a.m.1.2 | 4 | 39.38 | odd | 2 | |||
507.4.b.h.337.4 | 8 | 39.5 | even | 4 | |||
507.4.b.h.337.5 | 8 | 39.8 | even | 4 | |||
624.4.q.i.289.4 | 8 | 156.95 | even | 6 | |||
624.4.q.i.529.4 | 8 | 156.23 | even | 6 | |||
1521.4.a.v.1.3 | 4 | 13.12 | even | 2 | |||
1521.4.a.bb.1.2 | 4 | 1.1 | even | 1 | trivial |