Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{97}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 24 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.42443\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.42443 | −1.91783 | −0.958913 | − | 0.283702i | \(-0.908437\pi\) | ||||
−0.958913 | + | 0.283702i | \(0.908437\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 21.4244 | 2.67805 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −16.2733 | −1.10726 | ||||||||
\(7\) | 7.69772 | 0.415638 | 0.207819 | − | 0.978167i | \(-0.433364\pi\) | ||||
0.207819 | + | 0.978167i | \(0.433364\pi\) | |||||||
\(8\) | −72.8199 | −3.21821 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 64.2733 | 1.54617 | ||||||||
\(13\) | −24.8489 | −0.530141 | −0.265071 | − | 0.964229i | \(-0.585395\pi\) | ||||
−0.265071 | + | 0.964229i | \(0.585395\pi\) | |||||||
\(14\) | −41.7557 | −0.797120 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 223.611 | 3.49392 | ||||||||
\(17\) | 15.9420 | 0.227441 | 0.113721 | − | 0.993513i | \(-0.463723\pi\) | ||||
0.113721 | + | 0.993513i | \(0.463723\pi\) | |||||||
\(18\) | −48.8199 | −0.639275 | ||||||||
\(19\) | 15.1511 | 0.182943 | 0.0914713 | − | 0.995808i | \(-0.470843\pi\) | ||||
0.0914713 | + | 0.995808i | \(0.470843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23.0931 | 0.239968 | ||||||||
\(22\) | 59.6687 | 0.578246 | ||||||||
\(23\) | −17.7557 | −0.160971 | −0.0804853 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804853 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(24\) | −218.460 | −1.85804 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 134.791 | 1.01672 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 164.919 | 1.11310 | ||||||||
\(29\) | −128.547 | −0.823121 | −0.411560 | − | 0.911383i | \(-0.635016\pi\) | ||||
−0.411560 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 219.395 | 1.27112 | 0.635558 | − | 0.772053i | \(-0.280770\pi\) | ||||
0.635558 | + | 0.772053i | \(0.280770\pi\) | |||||||
\(32\) | −630.402 | −3.48251 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | −86.4763 | −0.436193 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 192.820 | 0.892685 | ||||||||
\(37\) | −92.0703 | −0.409088 | −0.204544 | − | 0.978857i | \(-0.565571\pi\) | ||||
−0.204544 | + | 0.978857i | \(0.565571\pi\) | |||||||
\(38\) | −82.1863 | −0.350852 | ||||||||
\(39\) | −74.5466 | −0.306077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −459.942 | −1.75197 | −0.875986 | − | 0.482336i | \(-0.839788\pi\) | ||||
−0.875986 | + | 0.482336i | \(0.839788\pi\) | |||||||
\(42\) | −125.267 | −0.460218 | ||||||||
\(43\) | −64.9648 | −0.230396 | −0.115198 | − | 0.993343i | \(-0.536750\pi\) | ||||
−0.115198 | + | 0.993343i | \(0.536750\pi\) | |||||||
\(44\) | −235.669 | −0.807464 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 96.3146 | 0.308713 | ||||||||
\(47\) | −497.408 | −1.54371 | −0.771855 | − | 0.635799i | \(-0.780671\pi\) | ||||
−0.771855 | + | 0.635799i | \(0.780671\pi\) | |||||||
\(48\) | 670.832 | 2.01721 | ||||||||
\(49\) | −283.745 | −0.827245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 47.8260 | 0.131313 | ||||||||
\(52\) | −532.373 | −1.41975 | ||||||||
\(53\) | 526.919 | 1.36562 | 0.682811 | − | 0.730596i | \(-0.260757\pi\) | ||||
0.682811 | + | 0.730596i | \(0.260757\pi\) | |||||||
\(54\) | −146.460 | −0.369086 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −560.547 | −1.33761 | ||||||||
\(57\) | 45.4534 | 0.105622 | ||||||||
\(58\) | 697.292 | 1.57860 | ||||||||
\(59\) | −578.443 | −1.27639 | −0.638194 | − | 0.769876i | \(-0.720318\pi\) | ||||
−0.638194 | + | 0.769876i | \(0.720318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −221.569 | −0.465067 | −0.232533 | − | 0.972588i | \(-0.574701\pi\) | ||||
−0.232533 | + | 0.972588i | \(0.574701\pi\) | |||||||
\(62\) | −1190.09 | −2.43778 | ||||||||
\(63\) | 69.2794 | 0.138546 | ||||||||
\(64\) | 1630.68 | 3.18493 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 179.006 | 0.333851 | ||||||||
\(67\) | 860.745 | 1.56950 | 0.784752 | − | 0.619810i | \(-0.212790\pi\) | ||||
0.784752 | + | 0.619810i | \(0.212790\pi\) | |||||||
\(68\) | 341.548 | 0.609100 | ||||||||
\(69\) | −53.2671 | −0.0929364 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 580.919 | 0.971020 | 0.485510 | − | 0.874231i | \(-0.338634\pi\) | ||||
0.485510 | + | 0.874231i | \(0.338634\pi\) | |||||||
\(72\) | −655.379 | −1.07274 | ||||||||
\(73\) | −510.116 | −0.817871 | −0.408935 | − | 0.912563i | \(-0.634100\pi\) | ||||
−0.408935 | + | 0.912563i | \(0.634100\pi\) | |||||||
\(74\) | 499.429 | 0.784560 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 324.605 | 0.489930 | ||||||||
\(77\) | −84.6749 | −0.125319 | ||||||||
\(78\) | 404.373 | 0.587002 | ||||||||
\(79\) | 1035.12 | 1.47418 | 0.737088 | − | 0.675797i | \(-0.236200\pi\) | ||||
0.737088 | + | 0.675797i | \(0.236200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 2494.92 | 3.35998 | ||||||||
\(83\) | −606.211 | −0.801690 | −0.400845 | − | 0.916146i | \(-0.631283\pi\) | ||||
−0.400845 | + | 0.916146i | \(0.631283\pi\) | |||||||
\(84\) | 494.757 | 0.642648 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 352.397 | 0.441860 | ||||||||
\(87\) | −385.640 | −0.475229 | ||||||||
\(88\) | 801.018 | 0.970328 | ||||||||
\(89\) | −23.4411 | −0.0279186 | −0.0139593 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139593 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −191.279 | −0.220347 | ||||||||
\(92\) | −380.406 | −0.431088 | ||||||||
\(93\) | 658.186 | 0.733879 | ||||||||
\(94\) | 2698.15 | 2.96057 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1891.20 | −2.01063 | ||||||||
\(97\) | −719.490 | −0.753126 | −0.376563 | − | 0.926391i | \(-0.622894\pi\) | ||||
−0.376563 | + | 0.926391i | \(0.622894\pi\) | |||||||
\(98\) | 1539.16 | 1.58651 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1871.27 | 1.84355 | 0.921774 | − | 0.387727i | \(-0.126740\pi\) | ||||
0.921774 | + | 0.387727i | \(0.126740\pi\) | |||||||
\(102\) | −259.429 | −0.251836 | ||||||||
\(103\) | 428.745 | 0.410151 | 0.205075 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205075 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(104\) | 1809.49 | 1.70611 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2858.24 | −2.61902 | ||||||||
\(107\) | −1148.02 | −1.03723 | −0.518616 | − | 0.855008i | \(-0.673552\pi\) | ||||
−0.518616 | + | 0.855008i | \(0.673552\pi\) | |||||||
\(108\) | 578.460 | 0.515392 | ||||||||
\(109\) | −1828.32 | −1.60662 | −0.803308 | − | 0.595564i | \(-0.796929\pi\) | ||||
−0.803308 | + | 0.595564i | \(0.796929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −276.211 | −0.236187 | ||||||||
\(112\) | 1721.29 | 1.45220 | ||||||||
\(113\) | −1126.40 | −0.937722 | −0.468861 | − | 0.883272i | \(-0.655335\pi\) | ||||
−0.468861 | + | 0.883272i | \(0.655335\pi\) | |||||||
\(114\) | −246.559 | −0.202565 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2754.04 | −2.20436 | ||||||||
\(117\) | −223.640 | −0.176714 | ||||||||
\(118\) | 3137.72 | 2.44789 | ||||||||
\(119\) | 122.717 | 0.0945332 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1201.89 | 0.891916 | ||||||||
\(123\) | −1379.83 | −1.01150 | ||||||||
\(124\) | 4700.42 | 3.40412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −375.801 | −0.265707 | ||||||||
\(127\) | −661.304 | −0.462057 | −0.231029 | − | 0.972947i | \(-0.574209\pi\) | ||||
−0.231029 | + | 0.972947i | \(0.574209\pi\) | |||||||
\(128\) | −3802.31 | −2.62562 | ||||||||
\(129\) | −194.895 | −0.133019 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 622.186 | 0.414967 | 0.207483 | − | 0.978239i | \(-0.433473\pi\) | ||||
0.207483 | + | 0.978239i | \(0.433473\pi\) | |||||||
\(132\) | −707.006 | −0.466189 | ||||||||
\(133\) | 116.629 | 0.0760378 | ||||||||
\(134\) | −4669.05 | −3.01003 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1160.89 | −0.731955 | ||||||||
\(137\) | 1872.84 | 1.16794 | 0.583969 | − | 0.811776i | \(-0.301499\pi\) | ||||
0.583969 | + | 0.811776i | \(0.301499\pi\) | |||||||
\(138\) | 288.944 | 0.178236 | ||||||||
\(139\) | −954.058 | −0.582174 | −0.291087 | − | 0.956697i | \(-0.594017\pi\) | ||||
−0.291087 | + | 0.956697i | \(0.594017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1492.22 | −0.891261 | ||||||||
\(142\) | −3151.15 | −1.86225 | ||||||||
\(143\) | 273.337 | 0.159844 | ||||||||
\(144\) | 2012.50 | 1.16464 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2767.09 | 1.56853 | ||||||||
\(147\) | −851.236 | −0.477610 | ||||||||
\(148\) | −1972.55 | −1.09556 | ||||||||
\(149\) | −2047.01 | −1.12549 | −0.562745 | − | 0.826631i | \(-0.690255\pi\) | ||||
−0.562745 | + | 0.826631i | \(0.690255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 475.863 | 0.256458 | 0.128229 | − | 0.991745i | \(-0.459071\pi\) | ||||
0.128229 | + | 0.991745i | \(0.459071\pi\) | |||||||
\(152\) | −1103.30 | −0.588749 | ||||||||
\(153\) | 143.478 | 0.0758138 | ||||||||
\(154\) | 459.313 | 0.240341 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1597.12 | −0.819691 | ||||||||
\(157\) | 647.466 | 0.329130 | 0.164565 | − | 0.986366i | \(-0.447378\pi\) | ||||
0.164565 | + | 0.986366i | \(0.447378\pi\) | |||||||
\(158\) | −5614.92 | −2.82721 | ||||||||
\(159\) | 1580.76 | 0.788442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −136.678 | −0.0669054 | ||||||||
\(162\) | −439.379 | −0.213092 | ||||||||
\(163\) | −1093.23 | −0.525329 | −0.262665 | − | 0.964887i | \(-0.584601\pi\) | ||||
−0.262665 | + | 0.964887i | \(0.584601\pi\) | |||||||
\(164\) | −9853.99 | −4.69188 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3288.35 | 1.53750 | ||||||||
\(167\) | −1123.25 | −0.520479 | −0.260240 | − | 0.965544i | \(-0.583802\pi\) | ||||
−0.260240 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(168\) | −1681.64 | −0.772270 | ||||||||
\(169\) | −1579.53 | −0.718951 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136.360 | 0.0609809 | ||||||||
\(172\) | −1391.83 | −0.617014 | ||||||||
\(173\) | −46.0123 | −0.0202211 | −0.0101106 | − | 0.999949i | \(-0.503218\pi\) | ||||
−0.0101106 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(174\) | 2091.88 | 0.911406 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2459.72 | −1.05346 | ||||||||
\(177\) | −1735.33 | −0.736923 | ||||||||
\(178\) | 127.155 | 0.0535430 | ||||||||
\(179\) | −831.975 | −0.347401 | −0.173700 | − | 0.984799i | \(-0.555572\pi\) | ||||
−0.173700 | + | 0.984799i | \(0.555572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1810.63 | −0.743553 | −0.371776 | − | 0.928322i | \(-0.621251\pi\) | ||||
−0.371776 | + | 0.928322i | \(0.621251\pi\) | |||||||
\(182\) | 1037.58 | 0.422586 | ||||||||
\(183\) | −664.708 | −0.268506 | ||||||||
\(184\) | 1292.97 | 0.518037 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3570.28 | −1.40745 | ||||||||
\(187\) | −175.362 | −0.0685762 | ||||||||
\(188\) | −10656.7 | −4.13414 | ||||||||
\(189\) | 207.838 | 0.0799895 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 458.898 | 0.173847 | 0.0869233 | − | 0.996215i | \(-0.472296\pi\) | ||||
0.0869233 | + | 0.996215i | \(0.472296\pi\) | |||||||
\(192\) | 4892.05 | 1.83882 | ||||||||
\(193\) | −1778.91 | −0.663465 | −0.331733 | − | 0.943373i | \(-0.607633\pi\) | ||||
−0.331733 | + | 0.943373i | \(0.607633\pi\) | |||||||
\(194\) | 3902.82 | 1.44436 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6079.08 | −2.21541 | ||||||||
\(197\) | −5304.53 | −1.91844 | −0.959218 | − | 0.282666i | \(-0.908781\pi\) | ||||
−0.959218 | + | 0.282666i | \(0.908781\pi\) | |||||||
\(198\) | 537.018 | 0.192749 | ||||||||
\(199\) | −5138.40 | −1.83041 | −0.915205 | − | 0.402989i | \(-0.867971\pi\) | ||||
−0.915205 | + | 0.402989i | \(0.867971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2582.24 | 0.906153 | ||||||||
\(202\) | −10150.6 | −3.53560 | ||||||||
\(203\) | −989.515 | −0.342120 | ||||||||
\(204\) | 1024.65 | 0.351664 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2325.70 | −0.786597 | ||||||||
\(207\) | −159.801 | −0.0536568 | ||||||||
\(208\) | −5556.47 | −1.85227 | ||||||||
\(209\) | −166.663 | −0.0551593 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4262.36 | −1.39068 | −0.695339 | − | 0.718682i | \(-0.744746\pi\) | ||||
−0.695339 | + | 0.718682i | \(0.744746\pi\) | |||||||
\(212\) | 11288.9 | 3.65721 | ||||||||
\(213\) | 1742.76 | 0.560619 | ||||||||
\(214\) | 6227.38 | 1.98923 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1966.14 | −0.619345 | ||||||||
\(217\) | 1688.84 | 0.528323 | ||||||||
\(218\) | 9917.58 | 3.08121 | ||||||||
\(219\) | −1530.35 | −0.472198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −396.141 | −0.120576 | ||||||||
\(222\) | 1498.29 | 0.452966 | ||||||||
\(223\) | 1377.80 | 0.413740 | 0.206870 | − | 0.978368i | \(-0.433672\pi\) | ||||
0.206870 | + | 0.978368i | \(0.433672\pi\) | |||||||
\(224\) | −4852.65 | −1.44746 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6110.06 | 1.79839 | ||||||||
\(227\) | 1227.28 | 0.358843 | 0.179422 | − | 0.983772i | \(-0.442577\pi\) | ||||
0.179422 | + | 0.983772i | \(0.442577\pi\) | |||||||
\(228\) | 973.814 | 0.282861 | ||||||||
\(229\) | 3890.28 | 1.12261 | 0.561304 | − | 0.827610i | \(-0.310300\pi\) | ||||
0.561304 | + | 0.827610i | \(0.310300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −254.025 | −0.0723532 | ||||||||
\(232\) | 9360.74 | 2.64898 | ||||||||
\(233\) | 3218.14 | 0.904837 | 0.452419 | − | 0.891806i | \(-0.350561\pi\) | ||||
0.452419 | + | 0.891806i | \(0.350561\pi\) | |||||||
\(234\) | 1213.12 | 0.338906 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12392.8 | −3.41823 | ||||||||
\(237\) | 3105.35 | 0.851115 | ||||||||
\(238\) | −665.670 | −0.181298 | ||||||||
\(239\) | −428.098 | −0.115864 | −0.0579318 | − | 0.998321i | \(-0.518451\pi\) | ||||
−0.0579318 | + | 0.998321i | \(0.518451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1231.16 | 0.329070 | 0.164535 | − | 0.986371i | \(-0.447388\pi\) | ||||
0.164535 | + | 0.986371i | \(0.447388\pi\) | |||||||
\(242\) | −656.356 | −0.174348 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −4747.00 | −1.24547 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7484.77 | 1.93988 | ||||||||
\(247\) | −376.489 | −0.0969854 | ||||||||
\(248\) | −15976.3 | −4.09072 | ||||||||
\(249\) | −1818.63 | −0.462856 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2838.22 | 0.713732 | 0.356866 | − | 0.934156i | \(-0.383845\pi\) | ||||
0.356866 | + | 0.934156i | \(0.383845\pi\) | |||||||
\(252\) | 1484.27 | 0.371033 | ||||||||
\(253\) | 195.313 | 0.0485344 | ||||||||
\(254\) | 3587.20 | 0.886145 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7579.90 | 1.85056 | ||||||||
\(257\) | −342.007 | −0.0830110 | −0.0415055 | − | 0.999138i | \(-0.513215\pi\) | ||||
−0.0415055 | + | 0.999138i | \(0.513215\pi\) | |||||||
\(258\) | 1057.19 | 0.255108 | ||||||||
\(259\) | −708.731 | −0.170032 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1156.92 | −0.274374 | ||||||||
\(262\) | −3375.01 | −0.795834 | ||||||||
\(263\) | −5895.00 | −1.38213 | −0.691067 | − | 0.722791i | \(-0.742859\pi\) | ||||
−0.691067 | + | 0.722791i | \(0.742859\pi\) | |||||||
\(264\) | 2403.06 | 0.560219 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −632.647 | −0.145827 | ||||||||
\(267\) | −70.3234 | −0.0161188 | ||||||||
\(268\) | 18441.0 | 4.20322 | ||||||||
\(269\) | −2496.18 | −0.565779 | −0.282890 | − | 0.959152i | \(-0.591293\pi\) | ||||
−0.282890 | + | 0.959152i | \(0.591293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2249.68 | −0.504274 | −0.252137 | − | 0.967692i | \(-0.581133\pi\) | ||||
−0.252137 | + | 0.967692i | \(0.581133\pi\) | |||||||
\(272\) | 3564.80 | 0.794662 | ||||||||
\(273\) | −573.838 | −0.127217 | ||||||||
\(274\) | −10159.1 | −2.23990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1141.22 | −0.248889 | ||||||||
\(277\) | −4082.59 | −0.885556 | −0.442778 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442778 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(278\) | 5175.22 | 1.11651 | ||||||||
\(279\) | 1974.56 | 0.423705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1033.79 | −0.219468 | −0.109734 | − | 0.993961i | \(-0.535000\pi\) | ||||
−0.109734 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(282\) | 8094.46 | 1.70928 | ||||||||
\(283\) | 7809.14 | 1.64030 | 0.820150 | − | 0.572148i | \(-0.193890\pi\) | ||||
0.820150 | + | 0.572148i | \(0.193890\pi\) | |||||||
\(284\) | 12445.9 | 2.60044 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1482.70 | −0.306552 | ||||||||
\(287\) | −3540.50 | −0.728186 | ||||||||
\(288\) | −5673.61 | −1.16084 | ||||||||
\(289\) | −4658.85 | −0.948270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2158.47 | −0.434817 | ||||||||
\(292\) | −10928.9 | −2.19030 | ||||||||
\(293\) | 1949.19 | 0.388645 | 0.194323 | − | 0.980938i | \(-0.437749\pi\) | ||||
0.194323 | + | 0.980938i | \(0.437749\pi\) | |||||||
\(294\) | 4617.47 | 0.915973 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6704.55 | 1.31653 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 11103.9 | 2.15849 | ||||||||
\(299\) | 441.209 | 0.0853371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −500.081 | −0.0957614 | ||||||||
\(302\) | −2581.28 | −0.491842 | ||||||||
\(303\) | 5613.81 | 1.06437 | ||||||||
\(304\) | 3387.96 | 0.639187 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −778.286 | −0.145398 | ||||||||
\(307\) | −2364.09 | −0.439497 | −0.219748 | − | 0.975557i | \(-0.570524\pi\) | ||||
−0.219748 | + | 0.975557i | \(0.570524\pi\) | |||||||
\(308\) | −1814.11 | −0.335612 | ||||||||
\(309\) | 1286.24 | 0.236801 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1989.17 | −0.362686 | −0.181343 | − | 0.983420i | \(-0.558044\pi\) | ||||
−0.181343 | + | 0.983420i | \(0.558044\pi\) | |||||||
\(312\) | 5428.47 | 0.985021 | ||||||||
\(313\) | 3878.67 | 0.700433 | 0.350216 | − | 0.936669i | \(-0.386108\pi\) | ||||
0.350216 | + | 0.936669i | \(0.386108\pi\) | |||||||
\(314\) | −3512.13 | −0.631214 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22176.8 | 3.94792 | ||||||||
\(317\) | −2913.73 | −0.516251 | −0.258126 | − | 0.966111i | \(-0.583105\pi\) | ||||
−0.258126 | + | 0.966111i | \(0.583105\pi\) | |||||||
\(318\) | −8574.71 | −1.51209 | ||||||||
\(319\) | 1414.01 | 0.248180 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3444.07 | −0.598846 | ||||||||
\(322\) | 741.402 | 0.128313 | ||||||||
\(323\) | 241.540 | 0.0416087 | ||||||||
\(324\) | 1735.38 | 0.297562 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5930.17 | 1.00749 | ||||||||
\(327\) | −5484.95 | −0.927580 | ||||||||
\(328\) | 33492.9 | 5.63822 | ||||||||
\(329\) | −3828.90 | −0.641624 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8104.46 | 1.34580 | 0.672902 | − | 0.739731i | \(-0.265047\pi\) | ||||
0.672902 | + | 0.739731i | \(0.265047\pi\) | |||||||
\(332\) | −12987.7 | −2.14697 | ||||||||
\(333\) | −828.633 | −0.136363 | ||||||||
\(334\) | 6093.02 | 0.998189 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5163.88 | 0.838430 | ||||||||
\(337\) | −5919.19 | −0.956792 | −0.478396 | − | 0.878144i | \(-0.658782\pi\) | ||||
−0.478396 | + | 0.878144i | \(0.658782\pi\) | |||||||
\(338\) | 8568.07 | 1.37882 | ||||||||
\(339\) | −3379.19 | −0.541394 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2413.35 | −0.383256 | ||||||||
\(342\) | −739.677 | −0.116951 | ||||||||
\(343\) | −4824.51 | −0.759472 | ||||||||
\(344\) | 4730.73 | 0.741465 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 249.590 | 0.0387805 | ||||||||
\(347\) | 8540.59 | 1.32128 | 0.660638 | − | 0.750705i | \(-0.270286\pi\) | ||||
0.660638 | + | 0.750705i | \(0.270286\pi\) | |||||||
\(348\) | −8262.11 | −1.27269 | ||||||||
\(349\) | 937.337 | 0.143767 | 0.0718833 | − | 0.997413i | \(-0.477099\pi\) | ||||
0.0718833 | + | 0.997413i | \(0.477099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −670.919 | −0.102026 | ||||||||
\(352\) | 6934.42 | 1.05002 | ||||||||
\(353\) | 211.118 | 0.0318319 | 0.0159160 | − | 0.999873i | \(-0.494934\pi\) | ||||
0.0159160 | + | 0.999873i | \(0.494934\pi\) | |||||||
\(354\) | 9413.17 | 1.41329 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −502.213 | −0.0747675 | ||||||||
\(357\) | 368.151 | 0.0545788 | ||||||||
\(358\) | 4512.99 | 0.666254 | ||||||||
\(359\) | −1376.31 | −0.202337 | −0.101169 | − | 0.994869i | \(-0.532258\pi\) | ||||
−0.101169 | + | 0.994869i | \(0.532258\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6629.44 | −0.966532 | ||||||||
\(362\) | 9821.63 | 1.42600 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | −4098.05 | −0.590100 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3605.66 | 0.514948 | ||||||||
\(367\) | −1030.45 | −0.146564 | −0.0732821 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732821 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(368\) | −3970.37 | −0.562418 | ||||||||
\(369\) | −4139.48 | −0.583991 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4056.07 | 0.567603 | ||||||||
\(372\) | 14101.3 | 1.96537 | ||||||||
\(373\) | −9365.39 | −1.30006 | −0.650029 | − | 0.759909i | \(-0.725243\pi\) | ||||
−0.650029 | + | 0.759909i | \(0.725243\pi\) | |||||||
\(374\) | 951.239 | 0.131517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 36221.2 | 4.96799 | ||||||||
\(377\) | 3194.24 | 0.436370 | ||||||||
\(378\) | −1127.40 | −0.153406 | ||||||||
\(379\) | −7120.23 | −0.965017 | −0.482509 | − | 0.875891i | \(-0.660274\pi\) | ||||
−0.482509 | + | 0.875891i | \(0.660274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1983.91 | −0.266769 | ||||||||
\(382\) | −2489.26 | −0.333407 | ||||||||
\(383\) | 1163.56 | 0.155235 | 0.0776176 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776176 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(384\) | −11406.9 | −1.51590 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9649.57 | 1.27241 | ||||||||
\(387\) | −584.684 | −0.0767988 | ||||||||
\(388\) | −15414.7 | −2.01691 | ||||||||
\(389\) | −10958.9 | −1.42838 | −0.714188 | − | 0.699954i | \(-0.753204\pi\) | ||||
−0.714188 | + | 0.699954i | \(0.753204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −283.062 | −0.0366114 | ||||||||
\(392\) | 20662.3 | 2.66225 | ||||||||
\(393\) | 1866.56 | 0.239581 | ||||||||
\(394\) | 28774.0 | 3.67923 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2121.02 | −0.269155 | ||||||||
\(397\) | 2172.09 | 0.274595 | 0.137298 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137298 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(398\) | 27872.9 | 3.51041 | ||||||||
\(399\) | 349.888 | 0.0439005 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7830.71 | 0.975180 | 0.487590 | − | 0.873073i | \(-0.337876\pi\) | ||||
0.487590 | + | 0.873073i | \(0.337876\pi\) | |||||||
\(402\) | −14007.2 | −1.73784 | ||||||||
\(403\) | −5451.73 | −0.673870 | ||||||||
\(404\) | 40090.9 | 4.93712 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5367.55 | 0.656126 | ||||||||
\(407\) | 1012.77 | 0.123345 | ||||||||
\(408\) | −3482.68 | −0.422594 | ||||||||
\(409\) | −10731.2 | −1.29736 | −0.648682 | − | 0.761060i | \(-0.724679\pi\) | ||||
−0.648682 | + | 0.761060i | \(0.724679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5618.52 | 0.674309 | ||||||||
\(412\) | 9185.62 | 1.09841 | ||||||||
\(413\) | −4452.69 | −0.530515 | ||||||||
\(414\) | 866.831 | 0.102904 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15664.8 | 1.84622 | ||||||||
\(417\) | −2862.17 | −0.336118 | ||||||||
\(418\) | 904.049 | 0.105786 | ||||||||
\(419\) | −7315.88 | −0.852994 | −0.426497 | − | 0.904489i | \(-0.640252\pi\) | ||||
−0.426497 | + | 0.904489i | \(0.640252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12495.7 | −1.44657 | −0.723284 | − | 0.690551i | \(-0.757368\pi\) | ||||
−0.723284 | + | 0.690551i | \(0.757368\pi\) | |||||||
\(422\) | 23120.9 | 2.66708 | ||||||||
\(423\) | −4476.67 | −0.514570 | ||||||||
\(424\) | −38370.2 | −4.39486 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9453.46 | −1.07517 | ||||||||
\(427\) | −1705.58 | −0.193299 | ||||||||
\(428\) | −24595.8 | −2.77776 | ||||||||
\(429\) | 820.012 | 0.0922857 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6075.01 | 0.678939 | 0.339470 | − | 0.940617i | \(-0.389752\pi\) | ||||
0.339470 | + | 0.940617i | \(0.389752\pi\) | |||||||
\(432\) | 6037.49 | 0.672405 | ||||||||
\(433\) | −5641.79 | −0.626160 | −0.313080 | − | 0.949727i | \(-0.601361\pi\) | ||||
−0.313080 | + | 0.949727i | \(0.601361\pi\) | |||||||
\(434\) | −9161.01 | −1.01323 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −39170.7 | −4.30260 | ||||||||
\(437\) | −269.019 | −0.0294484 | ||||||||
\(438\) | 8301.26 | 0.905593 | ||||||||
\(439\) | 10897.0 | 1.18470 | 0.592351 | − | 0.805680i | \(-0.298200\pi\) | ||||
0.592351 | + | 0.805680i | \(0.298200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2553.71 | −0.275748 | ||||||||
\(442\) | 2148.84 | 0.231244 | ||||||||
\(443\) | 7720.83 | 0.828054 | 0.414027 | − | 0.910265i | \(-0.364122\pi\) | ||||
0.414027 | + | 0.910265i | \(0.364122\pi\) | |||||||
\(444\) | −5917.66 | −0.632522 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7473.76 | −0.793481 | ||||||||
\(447\) | −6141.04 | −0.649802 | ||||||||
\(448\) | 12552.5 | 1.32378 | ||||||||
\(449\) | −7473.86 | −0.785553 | −0.392776 | − | 0.919634i | \(-0.628485\pi\) | ||||
−0.392776 | + | 0.919634i | \(0.628485\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5059.36 | 0.528240 | ||||||||
\(452\) | −24132.4 | −2.51127 | ||||||||
\(453\) | 1427.59 | 0.148066 | ||||||||
\(454\) | −6657.29 | −0.688198 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3309.91 | −0.339914 | ||||||||
\(457\) | −11140.5 | −1.14033 | −0.570167 | − | 0.821529i | \(-0.693121\pi\) | ||||
−0.570167 | + | 0.821529i | \(0.693121\pi\) | |||||||
\(458\) | −21102.6 | −2.15296 | ||||||||
\(459\) | 430.434 | 0.0437711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14328.8 | 1.44763 | 0.723817 | − | 0.689992i | \(-0.242386\pi\) | ||||
0.723817 | + | 0.689992i | \(0.242386\pi\) | |||||||
\(462\) | 1377.94 | 0.138761 | ||||||||
\(463\) | −11760.7 | −1.18049 | −0.590246 | − | 0.807223i | \(-0.700969\pi\) | ||||
−0.590246 | + | 0.807223i | \(0.700969\pi\) | |||||||
\(464\) | −28744.4 | −2.87592 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17456.5 | −1.73532 | ||||||||
\(467\) | −11854.9 | −1.17469 | −0.587343 | − | 0.809338i | \(-0.699826\pi\) | ||||
−0.587343 | + | 0.809338i | \(0.699826\pi\) | |||||||
\(468\) | −4791.35 | −0.473249 | ||||||||
\(469\) | 6625.77 | 0.652345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1942.40 | 0.190023 | ||||||||
\(472\) | 42122.1 | 4.10769 | ||||||||
\(473\) | 714.613 | 0.0694671 | ||||||||
\(474\) | −16844.8 | −1.63229 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2629.14 | 0.253165 | ||||||||
\(477\) | 4742.27 | 0.455207 | ||||||||
\(478\) | 2322.19 | 0.222206 | ||||||||
\(479\) | −1324.68 | −0.126359 | −0.0631796 | − | 0.998002i | \(-0.520124\pi\) | ||||
−0.0631796 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2287.84 | 0.216874 | ||||||||
\(482\) | −6678.34 | −0.631100 | ||||||||
\(483\) | −410.035 | −0.0386278 | ||||||||
\(484\) | 2592.36 | 0.243459 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1318.14 | −0.123029 | ||||||||
\(487\) | −18636.4 | −1.73408 | −0.867040 | − | 0.498239i | \(-0.833980\pi\) | ||||
−0.867040 | + | 0.498239i | \(0.833980\pi\) | |||||||
\(488\) | 16134.7 | 1.49668 | ||||||||
\(489\) | −3279.70 | −0.303299 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 124.552 | 0.0114480 | 0.00572398 | − | 0.999984i | \(-0.498178\pi\) | ||||
0.00572398 | + | 0.999984i | \(0.498178\pi\) | |||||||
\(492\) | −29562.0 | −2.70886 | ||||||||
\(493\) | −2049.29 | −0.187212 | ||||||||
\(494\) | 2042.24 | 0.186001 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49059.2 | 4.44117 | ||||||||
\(497\) | 4471.75 | 0.403592 | ||||||||
\(498\) | 9865.04 | 0.887677 | ||||||||
\(499\) | 10230.2 | 0.917768 | 0.458884 | − | 0.888496i | \(-0.348249\pi\) | ||||
0.458884 | + | 0.888496i | \(0.348249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3369.76 | −0.300499 | ||||||||
\(502\) | −15395.7 | −1.36881 | ||||||||
\(503\) | −5150.81 | −0.456587 | −0.228294 | − | 0.973592i | \(-0.573315\pi\) | ||||
−0.228294 | + | 0.973592i | \(0.573315\pi\) | |||||||
\(504\) | −5044.92 | −0.445870 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1059.46 | −0.0930806 | ||||||||
\(507\) | −4738.60 | −0.415086 | ||||||||
\(508\) | −14168.1 | −1.23741 | ||||||||
\(509\) | −22.7715 | −0.00198296 | −0.000991481 | − | 1.00000i | \(-0.500316\pi\) | ||||
−0.000991481 | 1.00000i | \(0.500316\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3926.73 | −0.339938 | ||||||||
\(512\) | −10698.1 | −0.923429 | ||||||||
\(513\) | 409.081 | 0.0352073 | ||||||||
\(514\) | 1855.19 | 0.159201 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4175.50 | −0.356233 | ||||||||
\(517\) | 5471.49 | 0.465446 | ||||||||
\(518\) | 3844.46 | 0.326093 | ||||||||
\(519\) | −138.037 | −0.0116747 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21521.7 | 1.80976 | 0.904879 | − | 0.425669i | \(-0.139961\pi\) | ||||
0.904879 | + | 0.425669i | \(0.139961\pi\) | |||||||
\(522\) | 6275.63 | 0.526201 | ||||||||
\(523\) | −2923.36 | −0.244416 | −0.122208 | − | 0.992504i | \(-0.538998\pi\) | ||||
−0.122208 | + | 0.992504i | \(0.538998\pi\) | |||||||
\(524\) | 13330.0 | 1.11130 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31977.0 | 2.65069 | ||||||||
\(527\) | 3497.60 | 0.289104 | ||||||||
\(528\) | −7379.15 | −0.608213 | ||||||||
\(529\) | −11851.7 | −0.974088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5205.99 | −0.425462 | ||||||||
\(532\) | 2498.71 | 0.203633 | ||||||||
\(533\) | 11429.0 | 0.928792 | ||||||||
\(534\) | 381.464 | 0.0309130 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −62679.3 | −5.05100 | ||||||||
\(537\) | −2495.93 | −0.200572 | ||||||||
\(538\) | 13540.3 | 1.08507 | ||||||||
\(539\) | 3121.20 | 0.249424 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21272.8 | 1.69056 | 0.845278 | − | 0.534327i | \(-0.179435\pi\) | ||||
0.845278 | + | 0.534327i | \(0.179435\pi\) | |||||||
\(542\) | 12203.2 | 0.967108 | ||||||||
\(543\) | −5431.89 | −0.429290 | ||||||||
\(544\) | −10049.9 | −0.792067 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3112.75 | 0.243980 | ||||||||
\(547\) | 18730.5 | 1.46409 | 0.732046 | − | 0.681256i | \(-0.238566\pi\) | ||||
0.732046 | + | 0.681256i | \(0.238566\pi\) | |||||||
\(548\) | 40124.5 | 3.12780 | ||||||||
\(549\) | −1994.12 | −0.155022 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1947.63 | −0.150584 | ||||||||
\(552\) | 3878.91 | 0.299089 | ||||||||
\(553\) | 7968.04 | 0.612723 | ||||||||
\(554\) | 22145.7 | 1.69834 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20440.1 | −1.55909 | ||||||||
\(557\) | 18885.0 | 1.43659 | 0.718297 | − | 0.695736i | \(-0.244922\pi\) | ||||
0.718297 | + | 0.695736i | \(0.244922\pi\) | |||||||
\(558\) | −10710.9 | −0.812593 | ||||||||
\(559\) | 1614.30 | 0.122143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −526.086 | −0.0395925 | ||||||||
\(562\) | 5607.71 | 0.420902 | ||||||||
\(563\) | −10285.1 | −0.769922 | −0.384961 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384961 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(564\) | −31970.0 | −2.38685 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −42360.1 | −3.14581 | ||||||||
\(567\) | 623.515 | 0.0461820 | ||||||||
\(568\) | −42302.5 | −3.12495 | ||||||||
\(569\) | 18008.8 | 1.32683 | 0.663415 | − | 0.748251i | \(-0.269106\pi\) | ||||
0.663415 | + | 0.748251i | \(0.269106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7010.79 | −0.513822 | −0.256911 | − | 0.966435i | \(-0.582705\pi\) | ||||
−0.256911 | + | 0.966435i | \(0.582705\pi\) | |||||||
\(572\) | 5856.10 | 0.428070 | ||||||||
\(573\) | 1376.69 | 0.100370 | ||||||||
\(574\) | 19205.2 | 1.39653 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14676.1 | 1.06164 | ||||||||
\(577\) | 16398.9 | 1.18318 | 0.591589 | − | 0.806240i | \(-0.298501\pi\) | ||||
0.591589 | + | 0.806240i | \(0.298501\pi\) | |||||||
\(578\) | 25271.6 | 1.81862 | ||||||||
\(579\) | −5336.73 | −0.383052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4666.44 | −0.333213 | ||||||||
\(582\) | 11708.5 | 0.833903 | ||||||||
\(583\) | −5796.11 | −0.411750 | ||||||||
\(584\) | 37146.6 | 2.63208 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10573.3 | −0.745354 | ||||||||
\(587\) | −12823.5 | −0.901671 | −0.450836 | − | 0.892607i | \(-0.648874\pi\) | ||||
−0.450836 | + | 0.892607i | \(0.648874\pi\) | |||||||
\(588\) | −18237.2 | −1.27907 | ||||||||
\(589\) | 3324.09 | 0.232541 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15913.6 | −1.10761 | ||||||||
\(592\) | −20587.9 | −1.42932 | ||||||||
\(593\) | −16899.5 | −1.17029 | −0.585144 | − | 0.810929i | \(-0.698962\pi\) | ||||
−0.585144 | + | 0.810929i | \(0.698962\pi\) | |||||||
\(594\) | 1611.06 | 0.111284 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −43856.1 | −3.01412 | ||||||||
\(597\) | −15415.2 | −1.05679 | ||||||||
\(598\) | −2393.31 | −0.163662 | ||||||||
\(599\) | −15074.9 | −1.02829 | −0.514143 | − | 0.857704i | \(-0.671890\pi\) | ||||
−0.514143 | + | 0.857704i | \(0.671890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11418.8 | −0.775014 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(602\) | 2712.65 | 0.183654 | ||||||||
\(603\) | 7746.71 | 0.523168 | ||||||||
\(604\) | 10195.1 | 0.686809 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30451.7 | −2.04128 | ||||||||
\(607\) | 17952.8 | 1.20046 | 0.600232 | − | 0.799826i | \(-0.295075\pi\) | ||||
0.600232 | + | 0.799826i | \(0.295075\pi\) | |||||||
\(608\) | −9551.30 | −0.637100 | ||||||||
\(609\) | −2968.54 | −0.197523 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12360.0 | 0.818384 | ||||||||
\(612\) | 3073.94 | 0.203033 | ||||||||
\(613\) | −12528.9 | −0.825507 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(614\) | 12823.8 | 0.842878 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6166.01 | 0.403305 | ||||||||
\(617\) | 8586.10 | 0.560232 | 0.280116 | − | 0.959966i | \(-0.409627\pi\) | ||||
0.280116 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(618\) | −6977.09 | −0.454142 | ||||||||
\(619\) | 18415.4 | 1.19576 | 0.597882 | − | 0.801584i | \(-0.296009\pi\) | ||||
0.597882 | + | 0.801584i | \(0.296009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −479.404 | −0.0309788 | ||||||||
\(622\) | 10790.1 | 0.695569 | ||||||||
\(623\) | −180.443 | −0.0116040 | ||||||||
\(624\) | −16669.4 | −1.06941 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21039.6 | −1.34331 | ||||||||
\(627\) | −499.988 | −0.0318462 | ||||||||
\(628\) | 13871.6 | 0.881427 | ||||||||
\(629\) | −1467.79 | −0.0930436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2374.38 | 0.149798 | 0.0748989 | − | 0.997191i | \(-0.476137\pi\) | ||||
0.0748989 | + | 0.997191i | \(0.476137\pi\) | |||||||
\(632\) | −75377.1 | −4.74421 | ||||||||
\(633\) | −12787.1 | −0.802909 | ||||||||
\(634\) | 15805.3 | 0.990080 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 33866.8 | 2.11149 | ||||||||
\(637\) | 7050.74 | 0.438557 | ||||||||
\(638\) | −7670.21 | −0.475966 | ||||||||
\(639\) | 5228.27 | 0.323673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11086.0 | 0.683104 | 0.341552 | − | 0.939863i | \(-0.389047\pi\) | ||||
0.341552 | + | 0.939863i | \(0.389047\pi\) | |||||||
\(642\) | 18682.1 | 1.14848 | ||||||||
\(643\) | −19934.1 | −1.22259 | −0.611294 | − | 0.791403i | \(-0.709351\pi\) | ||||
−0.611294 | + | 0.791403i | \(0.709351\pi\) | |||||||
\(644\) | −2928.26 | −0.179176 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1310.21 | −0.0797983 | ||||||||
\(647\) | 30634.8 | 1.86148 | 0.930739 | − | 0.365684i | \(-0.119165\pi\) | ||||
0.930739 | + | 0.365684i | \(0.119165\pi\) | |||||||
\(648\) | −5898.41 | −0.357579 | ||||||||
\(649\) | 6362.87 | 0.384845 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5066.53 | 0.305028 | ||||||||
\(652\) | −23421.9 | −1.40686 | ||||||||
\(653\) | 9818.07 | 0.588378 | 0.294189 | − | 0.955747i | \(-0.404951\pi\) | ||||
0.294189 | + | 0.955747i | \(0.404951\pi\) | |||||||
\(654\) | 29752.7 | 1.77894 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −102848. | −6.12125 | ||||||||
\(657\) | −4591.04 | −0.272624 | ||||||||
\(658\) | 20769.6 | 1.23052 | ||||||||
\(659\) | 16478.5 | 0.974070 | 0.487035 | − | 0.873383i | \(-0.338078\pi\) | ||||
0.487035 | + | 0.873383i | \(0.338078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2958.12 | 0.174066 | 0.0870328 | − | 0.996205i | \(-0.472262\pi\) | ||||
0.0870328 | + | 0.996205i | \(0.472262\pi\) | |||||||
\(662\) | −43962.1 | −2.58102 | ||||||||
\(663\) | −1188.42 | −0.0696146 | ||||||||
\(664\) | 44144.2 | 2.58001 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4494.86 | 0.261520 | ||||||||
\(667\) | 2282.44 | 0.132498 | ||||||||
\(668\) | −24065.1 | −1.39387 | ||||||||
\(669\) | 4133.39 | 0.238873 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2437.26 | 0.140223 | ||||||||
\(672\) | −14558.0 | −0.835692 | ||||||||
\(673\) | 29960.3 | 1.71602 | 0.858012 | − | 0.513630i | \(-0.171700\pi\) | ||||
0.858012 | + | 0.513630i | \(0.171700\pi\) | |||||||
\(674\) | 32108.2 | 1.83496 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33840.6 | −1.92539 | ||||||||
\(677\) | 4514.73 | 0.256300 | 0.128150 | − | 0.991755i | \(-0.459096\pi\) | ||||
0.128150 | + | 0.991755i | \(0.459096\pi\) | |||||||
\(678\) | 18330.2 | 1.03830 | ||||||||
\(679\) | −5538.43 | −0.313027 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3681.84 | 0.207178 | ||||||||
\(682\) | 13091.0 | 0.735018 | ||||||||
\(683\) | 13555.7 | 0.759438 | 0.379719 | − | 0.925102i | \(-0.376021\pi\) | ||||
0.379719 | + | 0.925102i | \(0.376021\pi\) | |||||||
\(684\) | 2921.44 | 0.163310 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26170.2 | 1.45653 | ||||||||
\(687\) | 11670.8 | 0.648137 | ||||||||
\(688\) | −14526.8 | −0.804986 | ||||||||
\(689\) | −13093.3 | −0.723972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11471.3 | −0.631535 | −0.315768 | − | 0.948837i | \(-0.602262\pi\) | ||||
−0.315768 | + | 0.948837i | \(0.602262\pi\) | |||||||
\(692\) | −985.787 | −0.0541532 | ||||||||
\(693\) | −762.074 | −0.0417731 | ||||||||
\(694\) | −46327.8 | −2.53398 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 28082.2 | 1.52939 | ||||||||
\(697\) | −7332.40 | −0.398471 | ||||||||
\(698\) | −5084.52 | −0.275719 | ||||||||
\(699\) | 9654.41 | 0.522408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22229.0 | 1.19769 | 0.598843 | − | 0.800866i | \(-0.295627\pi\) | ||||
0.598843 | + | 0.800866i | \(0.295627\pi\) | |||||||
\(702\) | 3639.35 | 0.195667 | ||||||||
\(703\) | −1394.97 | −0.0748397 | ||||||||
\(704\) | −17937.5 | −0.960292 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1145.19 | −0.0610480 | ||||||||
\(707\) | 14404.5 | 0.766248 | ||||||||
\(708\) | −37178.4 | −1.97352 | ||||||||
\(709\) | −15081.2 | −0.798851 | −0.399426 | − | 0.916766i | \(-0.630790\pi\) | ||||
−0.399426 | + | 0.916766i | \(0.630790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9316.06 | 0.491392 | ||||||||
\(712\) | 1706.98 | 0.0898480 | ||||||||
\(713\) | −3895.52 | −0.204612 | ||||||||
\(714\) | −1997.01 | −0.104673 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17824.6 | −0.930358 | ||||||||
\(717\) | −1284.30 | −0.0668938 | ||||||||
\(718\) | 7465.71 | 0.388047 | ||||||||
\(719\) | −7399.80 | −0.383819 | −0.191910 | − | 0.981413i | \(-0.561468\pi\) | ||||
−0.191910 | + | 0.981413i | \(0.561468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3300.36 | 0.170474 | ||||||||
\(722\) | 35960.9 | 1.85364 | ||||||||
\(723\) | 3693.48 | 0.189989 | ||||||||
\(724\) | −38791.7 | −1.99127 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1969.07 | −0.100660 | ||||||||
\(727\) | −1705.77 | −0.0870202 | −0.0435101 | − | 0.999053i | \(-0.513854\pi\) | ||||
−0.0435101 | + | 0.999053i | \(0.513854\pi\) | |||||||
\(728\) | 13928.9 | 0.709122 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1035.67 | −0.0524017 | ||||||||
\(732\) | −14241.0 | −0.719074 | ||||||||
\(733\) | −37122.6 | −1.87061 | −0.935303 | − | 0.353847i | \(-0.884873\pi\) | ||||
−0.935303 | + | 0.353847i | \(0.884873\pi\) | |||||||
\(734\) | 5589.60 | 0.281084 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11193.2 | 0.560581 | ||||||||
\(737\) | −9468.20 | −0.473223 | ||||||||
\(738\) | 22454.3 | 1.11999 | ||||||||
\(739\) | 34256.3 | 1.70520 | 0.852598 | − | 0.522568i | \(-0.175026\pi\) | ||||
0.852598 | + | 0.522568i | \(0.175026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1129.47 | −0.0559945 | ||||||||
\(742\) | −22001.9 | −1.08856 | ||||||||
\(743\) | −1567.88 | −0.0774160 | −0.0387080 | − | 0.999251i | \(-0.512324\pi\) | ||||
−0.0387080 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(744\) | −47929.0 | −2.36178 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 50801.9 | 2.49328 | ||||||||
\(747\) | −5455.90 | −0.267230 | ||||||||
\(748\) | −3757.03 | −0.183651 | ||||||||
\(749\) | −8837.17 | −0.431112 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −955.613 | −0.0464325 | −0.0232163 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232163 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(752\) | −111226. | −5.39360 | ||||||||
\(753\) | 8514.65 | 0.412073 | ||||||||
\(754\) | −17326.9 | −0.836881 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4452.82 | 0.214216 | ||||||||
\(757\) | 14015.4 | 0.672918 | 0.336459 | − | 0.941698i | \(-0.390771\pi\) | ||||
0.336459 | + | 0.941698i | \(0.390771\pi\) | |||||||
\(758\) | 38623.2 | 1.85073 | ||||||||
\(759\) | 585.938 | 0.0280214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36271.0 | −1.72776 | −0.863879 | − | 0.503699i | \(-0.831972\pi\) | ||||
−0.863879 | + | 0.503699i | \(0.831972\pi\) | |||||||
\(762\) | 10761.6 | 0.511616 | ||||||||
\(763\) | −14073.9 | −0.667770 | ||||||||
\(764\) | 9831.63 | 0.465571 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6311.64 | −0.297714 | ||||||||
\(767\) | 14373.6 | 0.676665 | ||||||||
\(768\) | 22739.7 | 1.06842 | ||||||||
\(769\) | −18163.6 | −0.851749 | −0.425874 | − | 0.904782i | \(-0.640033\pi\) | ||||
−0.425874 | + | 0.904782i | \(0.640033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1026.02 | −0.0479264 | ||||||||
\(772\) | −38112.1 | −1.77680 | ||||||||
\(773\) | 8345.65 | 0.388321 | 0.194160 | − | 0.980970i | \(-0.437802\pi\) | ||||
0.194160 | + | 0.980970i | \(0.437802\pi\) | |||||||
\(774\) | 3171.57 | 0.147287 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 52393.2 | 2.42372 | ||||||||
\(777\) | −2126.19 | −0.0981683 | ||||||||
\(778\) | 59445.7 | 2.73937 | ||||||||
\(779\) | −6968.65 | −0.320510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6390.11 | −0.292774 | ||||||||
\(782\) | 1535.45 | 0.0702142 | ||||||||
\(783\) | −3470.76 | −0.158410 | ||||||||
\(784\) | −63448.5 | −2.89033 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10125.0 | −0.459475 | ||||||||
\(787\) | 22996.2 | 1.04158 | 0.520791 | − | 0.853684i | \(-0.325637\pi\) | ||||
0.520791 | + | 0.853684i | \(0.325637\pi\) | |||||||
\(788\) | −113647. | −5.13768 | ||||||||
\(789\) | −17685.0 | −0.797975 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8670.69 | −0.389752 | ||||||||
\(792\) | 7209.17 | 0.323443 | ||||||||
\(793\) | 5505.75 | 0.246551 | ||||||||
\(794\) | −11782.4 | −0.526626 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −110087. | −4.90194 | ||||||||
\(797\) | 2743.82 | 0.121946 | 0.0609730 | − | 0.998139i | \(-0.480580\pi\) | ||||
0.0609730 | + | 0.998139i | \(0.480580\pi\) | |||||||
\(798\) | −1897.94 | −0.0841934 | ||||||||
\(799\) | −7929.68 | −0.351104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −210.970 | −0.00930619 | ||||||||
\(802\) | −42477.1 | −1.87022 | ||||||||
\(803\) | 5611.28 | 0.246597 | ||||||||
\(804\) | 55322.9 | 2.42673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 29572.5 | 1.29237 | ||||||||
\(807\) | −7488.53 | −0.326653 | ||||||||
\(808\) | −136266. | −5.93293 | ||||||||
\(809\) | 41241.7 | 1.79231 | 0.896156 | − | 0.443738i | \(-0.146348\pi\) | ||||
0.896156 | + | 0.443738i | \(0.146348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12832.9 | 0.555641 | 0.277820 | − | 0.960633i | \(-0.410388\pi\) | ||||
0.277820 | + | 0.960633i | \(0.410388\pi\) | |||||||
\(812\) | −21199.8 | −0.916215 | ||||||||
\(813\) | −6749.03 | −0.291142 | ||||||||
\(814\) | −5493.72 | −0.236554 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10694.4 | 0.458798 | ||||||||
\(817\) | −984.292 | −0.0421493 | ||||||||
\(818\) | 58210.4 | 2.48812 | ||||||||
\(819\) | −1721.51 | −0.0734488 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16368.5 | 0.695817 | 0.347908 | − | 0.937529i | \(-0.386892\pi\) | ||||
0.347908 | + | 0.937529i | \(0.386892\pi\) | |||||||
\(822\) | −30477.3 | −1.29321 | ||||||||
\(823\) | −3869.53 | −0.163892 | −0.0819461 | − | 0.996637i | \(-0.526114\pi\) | ||||
−0.0819461 | + | 0.996637i | \(0.526114\pi\) | |||||||
\(824\) | −31221.2 | −1.31995 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24153.3 | 1.01743 | ||||||||
\(827\) | −7388.69 | −0.310677 | −0.155339 | − | 0.987861i | \(-0.549647\pi\) | ||||
−0.155339 | + | 0.987861i | \(0.549647\pi\) | |||||||
\(828\) | −3423.65 | −0.143696 | ||||||||
\(829\) | 23990.1 | 1.00508 | 0.502539 | − | 0.864554i | \(-0.332399\pi\) | ||||
0.502539 | + | 0.864554i | \(0.332399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12247.8 | −0.511276 | ||||||||
\(832\) | −40520.6 | −1.68846 | ||||||||
\(833\) | −4523.47 | −0.188150 | ||||||||
\(834\) | 15525.7 | 0.644616 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3570.65 | −0.147720 | ||||||||
\(837\) | 5923.68 | 0.244626 | ||||||||
\(838\) | 39684.5 | 1.63589 | ||||||||
\(839\) | −18228.3 | −0.750074 | −0.375037 | − | 0.927010i | \(-0.622370\pi\) | ||||
−0.375037 | + | 0.927010i | \(0.622370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7864.78 | −0.322472 | ||||||||
\(842\) | 67782.3 | 2.77427 | ||||||||
\(843\) | −3101.36 | −0.126710 | ||||||||
\(844\) | −91318.7 | −3.72431 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24283.4 | 0.986855 | ||||||||
\(847\) | 931.424 | 0.0377852 | ||||||||
\(848\) | 117825. | 4.77137 | ||||||||
\(849\) | 23427.4 | 0.947028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1634.77 | 0.0658511 | ||||||||
\(852\) | 37337.6 | 1.50137 | ||||||||
\(853\) | 21737.3 | 0.872534 | 0.436267 | − | 0.899817i | \(-0.356300\pi\) | ||||
0.436267 | + | 0.899817i | \(0.356300\pi\) | |||||||
\(854\) | 9251.79 | 0.370714 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 83599.0 | 3.33803 | ||||||||
\(857\) | 18712.2 | 0.745852 | 0.372926 | − | 0.927861i | \(-0.378355\pi\) | ||||
0.372926 | + | 0.927861i | \(0.378355\pi\) | |||||||
\(858\) | −4448.10 | −0.176988 | ||||||||
\(859\) | 30527.6 | 1.21256 | 0.606279 | − | 0.795252i | \(-0.292661\pi\) | ||||
0.606279 | + | 0.795252i | \(0.292661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10621.5 | −0.420418 | ||||||||
\(862\) | −32953.4 | −1.30209 | ||||||||
\(863\) | −10906.4 | −0.430196 | −0.215098 | − | 0.976592i | \(-0.569007\pi\) | ||||
−0.215098 | + | 0.976592i | \(0.569007\pi\) | |||||||
\(864\) | −17020.8 | −0.670209 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30603.5 | 1.20087 | ||||||||
\(867\) | −13976.6 | −0.547484 | ||||||||
\(868\) | 36182.5 | 1.41488 | ||||||||
\(869\) | −11386.3 | −0.444481 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21388.5 | −0.832058 | ||||||||
\(872\) | 133138. | 5.17043 | ||||||||
\(873\) | −6475.41 | −0.251042 | ||||||||
\(874\) | 1459.28 | 0.0564768 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32786.8 | −1.26457 | ||||||||
\(877\) | −21770.9 | −0.838256 | −0.419128 | − | 0.907927i | \(-0.637664\pi\) | ||||
−0.419128 | + | 0.907927i | \(0.637664\pi\) | |||||||
\(878\) | −59109.8 | −2.27205 | ||||||||
\(879\) | 5847.58 | 0.224384 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47206.9 | 1.80527 | 0.902634 | − | 0.430409i | \(-0.141631\pi\) | ||||
0.902634 | + | 0.430409i | \(0.141631\pi\) | |||||||
\(882\) | 13852.4 | 0.528837 | ||||||||
\(883\) | 6059.68 | 0.230945 | 0.115473 | − | 0.993311i | \(-0.463162\pi\) | ||||
0.115473 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(884\) | −8487.09 | −0.322909 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41881.1 | −1.58806 | ||||||||
\(887\) | 37130.2 | 1.40553 | 0.702767 | − | 0.711420i | \(-0.251948\pi\) | ||||
0.702767 | + | 0.711420i | \(0.251948\pi\) | |||||||
\(888\) | 20113.6 | 0.760101 | ||||||||
\(889\) | −5090.53 | −0.192048 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 29518.5 | 1.10802 | ||||||||
\(893\) | −7536.30 | −0.282410 | ||||||||
\(894\) | 33311.6 | 1.24621 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29269.1 | −1.09131 | ||||||||
\(897\) | 1323.63 | 0.0492694 | ||||||||
\(898\) | 40541.4 | 1.50655 | ||||||||
\(899\) | −28202.5 | −1.04628 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8400.15 | 0.310599 | ||||||||
\(902\) | −27444.1 | −1.01307 | ||||||||
\(903\) | −1500.24 | −0.0552879 | ||||||||
\(904\) | 82024.1 | 3.01779 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7743.85 | −0.283965 | ||||||||
\(907\) | −1182.94 | −0.0433064 | −0.0216532 | − | 0.999766i | \(-0.506893\pi\) | ||||
−0.0216532 | + | 0.999766i | \(0.506893\pi\) | |||||||
\(908\) | 26293.8 | 0.961001 | ||||||||
\(909\) | 16841.4 | 0.614516 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37676.4 | 1.37022 | 0.685112 | − | 0.728438i | \(-0.259753\pi\) | ||||
0.685112 | + | 0.728438i | \(0.259753\pi\) | |||||||
\(912\) | 10163.9 | 0.369035 | ||||||||
\(913\) | 6668.32 | 0.241719 | ||||||||
\(914\) | 60431.1 | 2.18696 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 83347.1 | 3.00640 | ||||||||
\(917\) | 4789.41 | 0.172476 | ||||||||
\(918\) | −2334.86 | −0.0839454 | ||||||||
\(919\) | 8697.82 | 0.312203 | 0.156101 | − | 0.987741i | \(-0.450107\pi\) | ||||
0.156101 | + | 0.987741i | \(0.450107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7092.26 | −0.253744 | ||||||||
\(922\) | −77725.7 | −2.77631 | ||||||||
\(923\) | −14435.2 | −0.514778 | ||||||||
\(924\) | −5442.33 | −0.193766 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 63795.3 | 2.26398 | ||||||||
\(927\) | 3858.71 | 0.136717 | ||||||||
\(928\) | 81036.0 | 2.86653 | ||||||||
\(929\) | −17247.5 | −0.609119 | −0.304559 | − | 0.952493i | \(-0.598509\pi\) | ||||
−0.304559 | + | 0.952493i | \(0.598509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4299.06 | −0.151338 | ||||||||
\(932\) | 68946.7 | 2.42320 | ||||||||
\(933\) | −5967.51 | −0.209397 | ||||||||
\(934\) | 64306.0 | 2.25284 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16285.4 | 0.568702 | ||||||||
\(937\) | 41812.4 | 1.45779 | 0.728896 | − | 0.684624i | \(-0.240034\pi\) | ||||
0.728896 | + | 0.684624i | \(0.240034\pi\) | |||||||
\(938\) | −35941.0 | −1.25108 | ||||||||
\(939\) | 11636.0 | 0.404395 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37655.9 | 1.30451 | 0.652257 | − | 0.757998i | \(-0.273822\pi\) | ||||
0.652257 | + | 0.757998i | \(0.273822\pi\) | |||||||
\(942\) | −10536.4 | −0.364431 | ||||||||
\(943\) | 8166.60 | 0.282016 | ||||||||
\(944\) | −129346. | −4.45959 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3876.37 | −0.133226 | ||||||||
\(947\) | 21244.4 | 0.728986 | 0.364493 | − | 0.931206i | \(-0.381242\pi\) | ||||
0.364493 | + | 0.931206i | \(0.381242\pi\) | |||||||
\(948\) | 66530.4 | 2.27933 | ||||||||
\(949\) | 12675.8 | 0.433587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8741.20 | −0.298058 | ||||||||
\(952\) | −8936.24 | −0.304228 | ||||||||
\(953\) | −1324.27 | −0.0450130 | −0.0225065 | − | 0.999747i | \(-0.507165\pi\) | ||||
−0.0225065 | + | 0.999747i | \(0.507165\pi\) | |||||||
\(954\) | −25724.1 | −0.873007 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9171.77 | −0.310289 | ||||||||
\(957\) | 4242.04 | 0.143287 | ||||||||
\(958\) | 7185.62 | 0.242335 | ||||||||
\(959\) | 14416.6 | 0.485439 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18343.4 | 0.615735 | ||||||||
\(962\) | −12410.2 | −0.415927 | ||||||||
\(963\) | −10332.2 | −0.345744 | ||||||||
\(964\) | 26376.9 | 0.881268 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2224.21 | 0.0740815 | ||||||||
\(967\) | −52267.1 | −1.73815 | −0.869077 | − | 0.494676i | \(-0.835287\pi\) | ||||
−0.869077 | + | 0.494676i | \(0.835287\pi\) | |||||||
\(968\) | −8811.20 | −0.292565 | ||||||||
\(969\) | 724.619 | 0.0240228 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52489.8 | −1.73479 | −0.867394 | − | 0.497622i | \(-0.834207\pi\) | ||||
−0.867394 | + | 0.497622i | \(0.834207\pi\) | |||||||
\(972\) | 5206.14 | 0.171797 | ||||||||
\(973\) | −7344.07 | −0.241973 | ||||||||
\(974\) | 101092. | 3.32566 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −49545.3 | −1.62490 | ||||||||
\(977\) | −8324.11 | −0.272581 | −0.136291 | − | 0.990669i | \(-0.543518\pi\) | ||||
−0.136291 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(978\) | 17790.5 | 0.581675 | ||||||||
\(979\) | 257.852 | 0.00841777 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16454.9 | −0.535539 | ||||||||
\(982\) | −675.623 | −0.0219552 | ||||||||
\(983\) | 44407.1 | 1.44086 | 0.720431 | − | 0.693527i | \(-0.243944\pi\) | ||||
0.720431 | + | 0.693527i | \(0.243944\pi\) | |||||||
\(984\) | 100479. | 3.25523 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11116.2 | 0.359039 | ||||||||
\(987\) | −11486.7 | −0.370442 | ||||||||
\(988\) | −8066.05 | −0.259732 | ||||||||
\(989\) | 1153.50 | 0.0370870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45124.7 | −1.44645 | −0.723226 | − | 0.690612i | \(-0.757341\pi\) | ||||
−0.723226 | + | 0.690612i | \(0.757341\pi\) | |||||||
\(992\) | −138307. | −4.42667 | ||||||||
\(993\) | 24313.4 | 0.777001 | ||||||||
\(994\) | −24256.7 | −0.774020 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −38963.2 | −1.23955 | ||||||||
\(997\) | −5480.61 | −0.174095 | −0.0870474 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870474 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(998\) | −55492.9 | −1.76012 | ||||||||
\(999\) | −2485.90 | −0.0787291 |
(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 | 825.4.a.l.1.1 | 2 | ||
3.2 | odd | 2 | 2475.4.a.p.1.2 | 2 | |||
5.2 | odd | 4 | 825.4.c.h.199.1 | 4 | |||
5.3 | odd | 4 | 825.4.c.h.199.4 | 4 | |||
5.4 | even | 2 | 33.4.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 99.4.a.f.1.1 | 2 | |||
20.19 | odd | 2 | 528.4.a.p.1.1 | 2 | |||
35.34 | odd | 2 | 1617.4.a.k.1.2 | 2 | |||
40.19 | odd | 2 | 2112.4.a.bg.1.2 | 2 | |||
40.29 | even | 2 | 2112.4.a.bn.1.2 | 2 | |||
55.54 | odd | 2 | 363.4.a.i.1.1 | 2 | |||
60.59 | even | 2 | 1584.4.a.bj.1.2 | 2 | |||
165.164 | even | 2 | 1089.4.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
99.4.a.f.1.1 | 2 | 15.14 | odd | 2 | |||
363.4.a.i.1.1 | 2 | 55.54 | odd | 2 | |||
528.4.a.p.1.1 | 2 | 20.19 | odd | 2 | |||
825.4.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
825.4.c.h.199.1 | 4 | 5.2 | odd | 4 | |||
825.4.c.h.199.4 | 4 | 5.3 | odd | 4 | |||
1089.4.a.u.1.2 | 2 | 165.164 | even | 2 | |||
1584.4.a.bj.1.2 | 2 | 60.59 | even | 2 | |||
1617.4.a.k.1.2 | 2 | 35.34 | odd | 2 | |||
2112.4.a.bg.1.2 | 2 | 40.19 | odd | 2 | |||
2112.4.a.bn.1.2 | 2 | 40.29 | even | 2 | |||
2475.4.a.p.1.2 | 2 | 3.2 | odd | 2 |