Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.63855 | −1.28642 | −0.643210 | − | 0.765690i | \(-0.722398\pi\) | ||||
−0.643210 | + | 0.765690i | \(0.722398\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.23901 | 0.654877 | ||||||||
\(5\) | −13.7159 | −1.22678 | −0.613392 | − | 0.789779i | \(-0.710195\pi\) | ||||
−0.613392 | + | 0.789779i | \(0.710195\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.38539 | 0.398774 | 0.199387 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199387 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(8\) | 10.0460 | 0.443973 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 49.9058 | 1.57816 | ||||||||
\(11\) | −66.1642 | −1.81357 | −0.906785 | − | 0.421594i | \(-0.861471\pi\) | ||||
−0.906785 | + | 0.421594i | \(0.861471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.6111 | 0.567737 | 0.283869 | − | 0.958863i | \(-0.408382\pi\) | ||||
0.283869 | + | 0.958863i | \(0.408382\pi\) | |||||||
\(14\) | −26.8721 | −0.512990 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.4648 | −1.22601 | ||||||||
\(17\) | 49.9563 | 0.712716 | 0.356358 | − | 0.934349i | \(-0.384018\pi\) | ||||
0.356358 | + | 0.934349i | \(0.384018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.84240 | −0.118842 | −0.0594211 | − | 0.998233i | \(-0.518925\pi\) | ||||
−0.0594211 | + | 0.998233i | \(0.518925\pi\) | |||||||
\(20\) | −71.8575 | −0.803392 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 240.742 | 2.33301 | ||||||||
\(23\) | −14.3919 | −0.130475 | −0.0652375 | − | 0.997870i | \(-0.520780\pi\) | ||||
−0.0652375 | + | 0.997870i | \(0.520780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 63.1246 | 0.504997 | ||||||||
\(26\) | −96.8256 | −0.730348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 38.6922 | 0.261148 | ||||||||
\(29\) | −39.4988 | −0.252922 | −0.126461 | − | 0.991972i | \(-0.540362\pi\) | ||||
−0.126461 | + | 0.991972i | \(0.540362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −203.855 | −1.18108 | −0.590541 | − | 0.807008i | \(-0.701085\pi\) | ||||
−0.590541 | + | 0.807008i | \(0.701085\pi\) | |||||||
\(32\) | 205.130 | 1.13319 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −181.768 | −0.916852 | ||||||||
\(35\) | −101.297 | −0.489209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 386.423 | 1.71696 | 0.858481 | − | 0.512845i | \(-0.171408\pi\) | ||||
0.858481 | + | 0.512845i | \(0.171408\pi\) | |||||||
\(38\) | 35.8120 | 0.152881 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −137.789 | −0.544659 | ||||||||
\(41\) | 380.605 | 1.44977 | 0.724883 | − | 0.688871i | \(-0.241894\pi\) | ||||
0.724883 | + | 0.688871i | \(0.241894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 84.5120 | 0.299720 | 0.149860 | − | 0.988707i | \(-0.452118\pi\) | ||||
0.149860 | + | 0.988707i | \(0.452118\pi\) | |||||||
\(44\) | −346.635 | −1.18766 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 52.3657 | 0.167846 | ||||||||
\(47\) | −79.4396 | −0.246542 | −0.123271 | − | 0.992373i | \(-0.539338\pi\) | ||||
−0.123271 | + | 0.992373i | \(0.539338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −288.456 | −0.840980 | ||||||||
\(50\) | −229.682 | −0.649638 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 139.416 | 0.371798 | ||||||||
\(53\) | −549.481 | −1.42409 | −0.712047 | − | 0.702132i | \(-0.752232\pi\) | ||||
−0.712047 | + | 0.702132i | \(0.752232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 907.499 | 2.22486 | ||||||||
\(56\) | 74.1934 | 0.177045 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 143.718 | 0.325364 | ||||||||
\(59\) | −375.200 | −0.827914 | −0.413957 | − | 0.910296i | \(-0.635854\pi\) | ||||
−0.413957 | + | 0.910296i | \(0.635854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 461.499 | 0.968670 | 0.484335 | − | 0.874883i | \(-0.339062\pi\) | ||||
0.484335 | + | 0.874883i | \(0.339062\pi\) | |||||||
\(62\) | 741.737 | 1.51937 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −118.657 | −0.231751 | ||||||||
\(65\) | −364.993 | −0.696490 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −141.327 | −0.257699 | −0.128849 | − | 0.991664i | \(-0.541128\pi\) | ||||
−0.128849 | + | 0.991664i | \(0.541128\pi\) | |||||||
\(68\) | 261.722 | 0.466741 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 368.573 | 0.629328 | ||||||||
\(71\) | 164.404 | 0.274805 | 0.137402 | − | 0.990515i | \(-0.456125\pi\) | ||||
0.137402 | + | 0.990515i | \(0.456125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −830.189 | −1.33105 | −0.665523 | − | 0.746378i | \(-0.731791\pi\) | ||||
−0.665523 | + | 0.746378i | \(0.731791\pi\) | |||||||
\(74\) | −1406.02 | −2.20874 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −51.5645 | −0.0778270 | ||||||||
\(77\) | −488.649 | −0.723204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 979.054 | 1.39433 | 0.697166 | − | 0.716910i | \(-0.254444\pi\) | ||||
0.697166 | + | 0.716910i | \(0.254444\pi\) | |||||||
\(80\) | 1076.21 | 1.50405 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1384.85 | −1.86501 | ||||||||
\(83\) | 933.690 | 1.23477 | 0.617384 | − | 0.786662i | \(-0.288192\pi\) | ||||
0.617384 | + | 0.786662i | \(0.288192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −685.193 | −0.874348 | ||||||||
\(86\) | −307.501 | −0.385566 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −664.684 | −0.805177 | ||||||||
\(89\) | 647.053 | 0.770646 | 0.385323 | − | 0.922782i | \(-0.374090\pi\) | ||||
0.385323 | + | 0.922782i | \(0.374090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 196.533 | 0.226399 | ||||||||
\(92\) | −75.3995 | −0.0854450 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 289.044 | 0.317156 | ||||||||
\(95\) | 134.997 | 0.145794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 559.455 | 0.585608 | 0.292804 | − | 0.956172i | \(-0.405412\pi\) | ||||
0.292804 | + | 0.956172i | \(0.405412\pi\) | |||||||
\(98\) | 1049.56 | 1.08185 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 330.711 | 0.330711 | ||||||||
\(101\) | 1070.07 | 1.05422 | 0.527110 | − | 0.849797i | \(-0.323276\pi\) | ||||
0.527110 | + | 0.849797i | \(0.323276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1260.22 | −1.20557 | −0.602784 | − | 0.797904i | \(-0.705942\pi\) | ||||
−0.602784 | + | 0.797904i | \(0.705942\pi\) | |||||||
\(104\) | 267.334 | 0.252060 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1999.31 | 1.83198 | ||||||||
\(107\) | 1776.77 | 1.60530 | 0.802648 | − | 0.596453i | \(-0.203424\pi\) | ||||
0.802648 | + | 0.596453i | \(0.203424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1002.40 | 0.880853 | 0.440426 | − | 0.897789i | \(-0.354827\pi\) | ||||
0.440426 | + | 0.897789i | \(0.354827\pi\) | |||||||
\(110\) | −3301.98 | −2.86210 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −579.493 | −0.488902 | ||||||||
\(113\) | −936.016 | −0.779230 | −0.389615 | − | 0.920978i | \(-0.627392\pi\) | ||||
−0.389615 | + | 0.920978i | \(0.627392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 197.397 | 0.160064 | ||||||||
\(116\) | −206.935 | −0.165633 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1365.18 | 1.06505 | ||||||||
\(119\) | 368.946 | 0.284212 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3046.71 | 2.28903 | ||||||||
\(122\) | −1679.18 | −1.24612 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1068.00 | −0.773463 | ||||||||
\(125\) | 848.674 | 0.607262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −66.9696 | −0.0467921 | −0.0233960 | − | 0.999726i | \(-0.507448\pi\) | ||||
−0.0233960 | + | 0.999726i | \(0.507448\pi\) | |||||||
\(128\) | −1209.30 | −0.835065 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1328.05 | 0.895979 | ||||||||
\(131\) | −438.635 | −0.292548 | −0.146274 | − | 0.989244i | \(-0.546728\pi\) | ||||
−0.146274 | + | 0.989244i | \(0.546728\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −72.6899 | −0.0473911 | ||||||||
\(134\) | 514.224 | 0.331509 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 501.859 | 0.316427 | ||||||||
\(137\) | 694.908 | 0.433358 | 0.216679 | − | 0.976243i | \(-0.430478\pi\) | ||||
0.216679 | + | 0.976243i | \(0.430478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2166.57 | −1.32206 | −0.661030 | − | 0.750359i | \(-0.729881\pi\) | ||||
−0.661030 | + | 0.750359i | \(0.729881\pi\) | |||||||
\(140\) | −530.696 | −0.320371 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −598.190 | −0.353514 | ||||||||
\(143\) | −1760.70 | −1.02963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 541.760 | 0.310281 | ||||||||
\(146\) | 3020.68 | 1.71228 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2024.48 | 1.12440 | ||||||||
\(149\) | −129.578 | −0.0712448 | −0.0356224 | − | 0.999365i | \(-0.511341\pi\) | ||||
−0.0356224 | + | 0.999365i | \(0.511341\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1086.93 | 0.585784 | 0.292892 | − | 0.956145i | \(-0.405382\pi\) | ||||
0.292892 | + | 0.956145i | \(0.405382\pi\) | |||||||
\(152\) | −98.8764 | −0.0527627 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1777.97 | 0.930344 | ||||||||
\(155\) | 2796.05 | 1.44893 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −840.599 | −0.427306 | −0.213653 | − | 0.976910i | \(-0.568536\pi\) | ||||
−0.213653 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(158\) | −3562.33 | −1.79370 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2813.53 | −1.39018 | ||||||||
\(161\) | −106.290 | −0.0520300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1448.81 | 0.696191 | 0.348096 | − | 0.937459i | \(-0.386828\pi\) | ||||
0.348096 | + | 0.937459i | \(0.386828\pi\) | |||||||
\(164\) | 1993.99 | 0.949419 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3397.27 | −1.58843 | ||||||||
\(167\) | 2941.59 | 1.36304 | 0.681519 | − | 0.731801i | \(-0.261320\pi\) | ||||
0.681519 | + | 0.731801i | \(0.261320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1488.85 | −0.677675 | ||||||||
\(170\) | 2493.10 | 1.12478 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 442.759 | 0.196280 | ||||||||
\(173\) | 929.288 | 0.408396 | 0.204198 | − | 0.978930i | \(-0.434541\pi\) | ||||
0.204198 | + | 0.978930i | \(0.434541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 466.200 | 0.201379 | ||||||||
\(176\) | 5191.57 | 2.22346 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2354.33 | −0.991374 | ||||||||
\(179\) | 3981.41 | 1.66248 | 0.831242 | − | 0.555910i | \(-0.187630\pi\) | ||||
0.831242 | + | 0.555910i | \(0.187630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 467.477 | 0.191974 | 0.0959870 | − | 0.995383i | \(-0.469399\pi\) | ||||
0.0959870 | + | 0.995383i | \(0.469399\pi\) | |||||||
\(182\) | −715.095 | −0.291244 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −144.581 | −0.0579274 | ||||||||
\(185\) | −5300.13 | −2.10634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3305.32 | −1.29256 | ||||||||
\(188\) | −416.185 | −0.161454 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −491.192 | −0.187552 | ||||||||
\(191\) | 252.008 | 0.0954695 | 0.0477347 | − | 0.998860i | \(-0.484800\pi\) | ||||
0.0477347 | + | 0.998860i | \(0.484800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3575.36 | −1.33347 | −0.666735 | − | 0.745295i | \(-0.732309\pi\) | ||||
−0.666735 | + | 0.745295i | \(0.732309\pi\) | |||||||
\(194\) | −2035.60 | −0.753338 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1511.23 | −0.550738 | ||||||||
\(197\) | −5474.34 | −1.97985 | −0.989924 | − | 0.141596i | \(-0.954776\pi\) | ||||
−0.989924 | + | 0.141596i | \(0.954776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4376.75 | 1.55909 | 0.779547 | − | 0.626343i | \(-0.215449\pi\) | ||||
0.779547 | + | 0.626343i | \(0.215449\pi\) | |||||||
\(200\) | 634.148 | 0.224205 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3893.51 | −1.35617 | ||||||||
\(203\) | −291.714 | −0.100859 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5220.32 | −1.77855 | ||||||||
\(206\) | 4585.38 | 1.55087 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2088.03 | −0.696053 | ||||||||
\(209\) | 651.215 | 0.215528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1372.80 | 0.447902 | 0.223951 | − | 0.974600i | \(-0.428105\pi\) | ||||
0.223951 | + | 0.974600i | \(0.428105\pi\) | |||||||
\(212\) | −2878.74 | −0.932607 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6464.85 | −2.06509 | ||||||||
\(215\) | −1159.15 | −0.367691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1505.55 | −0.470984 | ||||||||
\(218\) | −3647.30 | −1.13315 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4754.40 | 1.45701 | ||||||||
\(221\) | 1329.39 | 0.404635 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −810.858 | −0.243494 | −0.121747 | − | 0.992561i | \(-0.538850\pi\) | ||||
−0.121747 | + | 0.992561i | \(0.538850\pi\) | |||||||
\(224\) | 1514.97 | 0.451888 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3405.74 | 1.00242 | ||||||||
\(227\) | 3355.29 | 0.981049 | 0.490525 | − | 0.871427i | \(-0.336805\pi\) | ||||
0.490525 | + | 0.871427i | \(0.336805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3126.00 | −0.902061 | −0.451031 | − | 0.892508i | \(-0.648944\pi\) | ||||
−0.451031 | + | 0.892508i | \(0.648944\pi\) | |||||||
\(230\) | −718.240 | −0.205910 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −396.804 | −0.112291 | ||||||||
\(233\) | −2978.06 | −0.837335 | −0.418667 | − | 0.908140i | \(-0.637503\pi\) | ||||
−0.418667 | + | 0.908140i | \(0.637503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1089.58 | 0.302453 | ||||||||
\(236\) | −1965.68 | −0.542182 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1342.43 | −0.365616 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3128.78 | −0.836276 | −0.418138 | − | 0.908383i | \(-0.637317\pi\) | ||||
−0.418138 | + | 0.908383i | \(0.637317\pi\) | |||||||
\(242\) | −11085.6 | −2.94466 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2417.80 | 0.634360 | ||||||||
\(245\) | 3956.42 | 1.03170 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −261.917 | −0.0674711 | ||||||||
\(248\) | −2047.93 | −0.524369 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3087.94 | −0.781194 | ||||||||
\(251\) | 4509.62 | 1.13404 | 0.567021 | − | 0.823703i | \(-0.308096\pi\) | ||||
0.567021 | + | 0.823703i | \(0.308096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 952.231 | 0.236625 | ||||||||
\(254\) | 243.672 | 0.0601943 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5349.36 | 1.30600 | ||||||||
\(257\) | 5048.58 | 1.22538 | 0.612688 | − | 0.790324i | \(-0.290088\pi\) | ||||
0.612688 | + | 0.790324i | \(0.290088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2853.89 | 0.684679 | ||||||||
\(260\) | −1912.21 | −0.456115 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1595.99 | 0.376339 | ||||||||
\(263\) | 4417.95 | 1.03583 | 0.517913 | − | 0.855433i | \(-0.326709\pi\) | ||||
0.517913 | + | 0.855433i | \(0.326709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7536.60 | 1.74706 | ||||||||
\(266\) | 264.486 | 0.0609649 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −740.413 | −0.168761 | ||||||||
\(269\) | −2139.43 | −0.484919 | −0.242460 | − | 0.970161i | \(-0.577954\pi\) | ||||
−0.242460 | + | 0.970161i | \(0.577954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3607.43 | 0.808619 | 0.404310 | − | 0.914622i | \(-0.367512\pi\) | ||||
0.404310 | + | 0.914622i | \(0.367512\pi\) | |||||||
\(272\) | −3919.81 | −0.873799 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2528.46 | −0.557480 | ||||||||
\(275\) | −4176.59 | −0.915847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8502.58 | −1.84430 | −0.922149 | − | 0.386835i | \(-0.873568\pi\) | ||||
−0.922149 | + | 0.386835i | \(0.873568\pi\) | |||||||
\(278\) | 7883.18 | 1.70073 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1017.63 | −0.217196 | ||||||||
\(281\) | −1837.65 | −0.390124 | −0.195062 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195062 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7370.66 | 1.54820 | 0.774099 | − | 0.633064i | \(-0.218203\pi\) | ||||
0.774099 | + | 0.633064i | \(0.218203\pi\) | |||||||
\(284\) | 861.313 | 0.179963 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6406.39 | 1.32454 | ||||||||
\(287\) | 2810.91 | 0.578129 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2417.37 | −0.492036 | ||||||||
\(290\) | −1971.22 | −0.399152 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4349.37 | −0.871671 | ||||||||
\(293\) | −952.999 | −0.190016 | −0.0950081 | − | 0.995476i | \(-0.530288\pi\) | ||||
−0.0950081 | + | 0.995476i | \(0.530288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5146.19 | 1.01567 | ||||||||
\(296\) | 3882.00 | 0.762286 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 471.477 | 0.0916508 | ||||||||
\(299\) | −382.984 | −0.0740755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 624.154 | 0.119520 | ||||||||
\(302\) | −3954.86 | −0.753565 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 772.282 | 0.145702 | ||||||||
\(305\) | −6329.85 | −1.18835 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −949.397 | −0.176498 | −0.0882491 | − | 0.996098i | \(-0.528127\pi\) | ||||
−0.0882491 | + | 0.996098i | \(0.528127\pi\) | |||||||
\(308\) | −2560.04 | −0.473609 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10173.6 | −1.86393 | ||||||||
\(311\) | −5917.05 | −1.07886 | −0.539429 | − | 0.842031i | \(-0.681360\pi\) | ||||
−0.539429 | + | 0.842031i | \(0.681360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1078.16 | 0.194701 | 0.0973506 | − | 0.995250i | \(-0.468963\pi\) | ||||
0.0973506 | + | 0.995250i | \(0.468963\pi\) | |||||||
\(314\) | 3058.56 | 0.549695 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5129.28 | 0.913115 | ||||||||
\(317\) | −6420.27 | −1.13753 | −0.568767 | − | 0.822499i | \(-0.692579\pi\) | ||||
−0.568767 | + | 0.822499i | \(0.692579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2613.41 | 0.458692 | ||||||||
\(320\) | 1627.48 | 0.284308 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 386.741 | 0.0669324 | ||||||||
\(323\) | −491.689 | −0.0847007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1679.81 | 0.286705 | ||||||||
\(326\) | −5271.54 | −0.895595 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3823.54 | 0.643658 | ||||||||
\(329\) | −586.692 | −0.0983142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2171.66 | −0.360620 | −0.180310 | − | 0.983610i | \(-0.557710\pi\) | ||||
−0.180310 | + | 0.983610i | \(0.557710\pi\) | |||||||
\(332\) | 4891.61 | 0.808621 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10703.1 | −1.75344 | ||||||||
\(335\) | 1938.42 | 0.316140 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4470.30 | −0.722591 | −0.361295 | − | 0.932451i | \(-0.617665\pi\) | ||||
−0.361295 | + | 0.932451i | \(0.617665\pi\) | |||||||
\(338\) | 5417.25 | 0.871774 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3589.73 | −0.572590 | ||||||||
\(341\) | 13487.9 | 2.14197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4663.55 | −0.734134 | ||||||||
\(344\) | 849.005 | 0.133068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3381.26 | −0.525369 | ||||||||
\(347\) | −275.767 | −0.0426626 | −0.0213313 | − | 0.999772i | \(-0.506790\pi\) | ||||
−0.0213313 | + | 0.999772i | \(0.506790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6311.44 | −0.968033 | −0.484017 | − | 0.875059i | \(-0.660823\pi\) | ||||
−0.484017 | + | 0.875059i | \(0.660823\pi\) | |||||||
\(350\) | −1696.29 | −0.259058 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13572.3 | −2.05513 | ||||||||
\(353\) | −452.697 | −0.0682568 | −0.0341284 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341284 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2254.94 | −0.337126 | ||||||||
\(356\) | 3389.92 | 0.504678 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14486.6 | −2.13865 | ||||||||
\(359\) | −4.87452 | −0.000716622 0 | −0.000358311 | − | 1.00000i | \(-0.500114\pi\) | ||||
−0.000358311 | 1.00000i | \(0.500114\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6762.13 | −0.985877 | ||||||||
\(362\) | −1700.94 | −0.246959 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1029.64 | 0.148263 | ||||||||
\(365\) | 11386.8 | 1.63290 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13316.3 | −1.89402 | −0.947012 | − | 0.321198i | \(-0.895914\pi\) | ||||
−0.947012 | + | 0.321198i | \(0.895914\pi\) | |||||||
\(368\) | 1129.26 | 0.159964 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19284.7 | 2.70964 | ||||||||
\(371\) | −4058.13 | −0.567891 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7061.40 | −0.980229 | −0.490115 | − | 0.871658i | \(-0.663045\pi\) | ||||
−0.490115 | + | 0.871658i | \(0.663045\pi\) | |||||||
\(374\) | 12026.5 | 1.66278 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −798.048 | −0.109458 | ||||||||
\(377\) | −1051.11 | −0.143593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13537.7 | 1.83479 | 0.917393 | − | 0.397982i | \(-0.130289\pi\) | ||||
0.917393 | + | 0.397982i | \(0.130289\pi\) | |||||||
\(380\) | 707.250 | 0.0954768 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −916.943 | −0.122814 | ||||||||
\(383\) | −6264.10 | −0.835720 | −0.417860 | − | 0.908511i | \(-0.637220\pi\) | ||||
−0.417860 | + | 0.908511i | \(0.637220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6702.23 | 0.887214 | ||||||||
\(386\) | 13009.1 | 1.71540 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2930.99 | 0.383501 | ||||||||
\(389\) | 6724.40 | 0.876455 | 0.438227 | − | 0.898864i | \(-0.355607\pi\) | ||||
0.438227 | + | 0.898864i | \(0.355607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −718.967 | −0.0929916 | ||||||||
\(392\) | −2897.82 | −0.373373 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19918.6 | 2.54692 | ||||||||
\(395\) | −13428.6 | −1.71054 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4578.31 | 0.578788 | 0.289394 | − | 0.957210i | \(-0.406546\pi\) | ||||
0.289394 | + | 0.957210i | \(0.406546\pi\) | |||||||
\(398\) | −15925.0 | −2.00565 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4953.06 | −0.619133 | ||||||||
\(401\) | −299.242 | −0.0372654 | −0.0186327 | − | 0.999826i | \(-0.505931\pi\) | ||||
−0.0186327 | + | 0.999826i | \(0.505931\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5424.81 | −0.670544 | ||||||||
\(404\) | 5606.13 | 0.690384 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1061.42 | 0.129747 | ||||||||
\(407\) | −25567.4 | −3.11383 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2314.81 | 0.279854 | 0.139927 | − | 0.990162i | \(-0.455313\pi\) | ||||
0.139927 | + | 0.990162i | \(0.455313\pi\) | |||||||
\(410\) | 18994.4 | 2.28796 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6602.33 | −0.789499 | ||||||||
\(413\) | −2771.00 | −0.330150 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12806.4 | −1.51479 | ||||||||
\(416\) | 5458.73 | 0.643357 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2369.47 | −0.277260 | ||||||||
\(419\) | −13789.0 | −1.60773 | −0.803864 | − | 0.594813i | \(-0.797226\pi\) | ||||
−0.803864 | + | 0.594813i | \(0.797226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6168.28 | −0.714071 | −0.357035 | − | 0.934091i | \(-0.616212\pi\) | ||||
−0.357035 | + | 0.934091i | \(0.616212\pi\) | |||||||
\(422\) | −4994.98 | −0.576190 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5520.07 | −0.632260 | ||||||||
\(425\) | 3153.47 | 0.359919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3408.35 | 0.386280 | ||||||||
\(428\) | 9308.52 | 1.05127 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4217.63 | 0.473005 | ||||||||
\(431\) | −4839.40 | −0.540849 | −0.270424 | − | 0.962741i | \(-0.587164\pi\) | ||||
−0.270424 | + | 0.962741i | \(0.587164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5275.54 | 0.585512 | 0.292756 | − | 0.956187i | \(-0.405428\pi\) | ||||
0.292756 | + | 0.956187i | \(0.405428\pi\) | |||||||
\(434\) | 5478.02 | 0.605883 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5251.61 | 0.576850 | ||||||||
\(437\) | 141.651 | 0.0155059 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8024.63 | −0.872425 | −0.436212 | − | 0.899844i | \(-0.643680\pi\) | ||||
−0.436212 | + | 0.899844i | \(0.643680\pi\) | |||||||
\(440\) | 9116.71 | 0.987777 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4837.04 | −0.520531 | ||||||||
\(443\) | −10024.2 | −1.07509 | −0.537544 | − | 0.843236i | \(-0.680648\pi\) | ||||
−0.537544 | + | 0.843236i | \(0.680648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8874.88 | −0.945415 | ||||||||
\(446\) | 2950.35 | 0.313235 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −876.325 | −0.0924163 | ||||||||
\(449\) | −11626.0 | −1.22197 | −0.610984 | − | 0.791643i | \(-0.709226\pi\) | ||||
−0.610984 | + | 0.791643i | \(0.709226\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25182.4 | −2.62925 | ||||||||
\(452\) | −4903.80 | −0.510300 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12208.4 | −1.26204 | ||||||||
\(455\) | −2695.62 | −0.277742 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8569.20 | 0.877134 | 0.438567 | − | 0.898698i | \(-0.355486\pi\) | ||||
0.438567 | + | 0.898698i | \(0.355486\pi\) | |||||||
\(458\) | 11374.1 | 1.16043 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1034.17 | 0.104822 | ||||||||
\(461\) | −15878.4 | −1.60419 | −0.802095 | − | 0.597197i | \(-0.796281\pi\) | ||||
−0.802095 | + | 0.597197i | \(0.796281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11333.4 | 1.13759 | 0.568796 | − | 0.822478i | \(-0.307409\pi\) | ||||
0.568796 | + | 0.822478i | \(0.307409\pi\) | |||||||
\(464\) | 3099.27 | 0.310086 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10835.8 | 1.07716 | ||||||||
\(467\) | 6065.43 | 0.601016 | 0.300508 | − | 0.953779i | \(-0.402844\pi\) | ||||
0.300508 | + | 0.953779i | \(0.402844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1043.75 | −0.102763 | ||||||||
\(470\) | −3964.49 | −0.389082 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3769.25 | −0.367572 | ||||||||
\(473\) | −5591.67 | −0.543563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −621.297 | −0.0600149 | ||||||||
\(476\) | 1932.92 | 0.186124 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 869.612 | 0.0832116 | ||||||||
\(479\) | 5215.54 | 0.497504 | 0.248752 | − | 0.968567i | \(-0.419980\pi\) | ||||
0.248752 | + | 0.968567i | \(0.419980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10283.1 | 0.974783 | ||||||||
\(482\) | 11384.2 | 1.07580 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15961.7 | 1.49904 | ||||||||
\(485\) | −7673.40 | −0.718414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15569.3 | −1.44869 | −0.724347 | − | 0.689435i | \(-0.757859\pi\) | ||||
−0.724347 | + | 0.689435i | \(0.757859\pi\) | |||||||
\(488\) | 4636.20 | 0.430064 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14395.6 | −1.32720 | ||||||||
\(491\) | −1285.69 | −0.118172 | −0.0590859 | − | 0.998253i | \(-0.518819\pi\) | ||||
−0.0590859 | + | 0.998253i | \(0.518819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1973.21 | −0.180262 | ||||||||
\(494\) | 952.996 | 0.0867962 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15995.5 | 1.44802 | ||||||||
\(497\) | 1214.18 | 0.109585 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2343.62 | 0.210250 | 0.105125 | − | 0.994459i | \(-0.466476\pi\) | ||||
0.105125 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(500\) | 4446.22 | 0.397682 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16408.4 | −1.45885 | ||||||||
\(503\) | −8604.12 | −0.762701 | −0.381351 | − | 0.924430i | \(-0.624541\pi\) | ||||
−0.381351 | + | 0.924430i | \(0.624541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14677.0 | −1.29330 | ||||||||
\(506\) | −3464.73 | −0.304400 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −350.855 | −0.0306430 | ||||||||
\(509\) | −12151.5 | −1.05817 | −0.529083 | − | 0.848570i | \(-0.677464\pi\) | ||||
−0.529083 | + | 0.848570i | \(0.677464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6131.27 | −0.530786 | ||||||||
\(512\) | −9789.46 | −0.844994 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18369.5 | −1.57635 | ||||||||
\(515\) | 17285.0 | 1.47897 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5256.06 | 0.447120 | ||||||||
\(518\) | −10384.0 | −0.880785 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3666.71 | −0.309223 | ||||||||
\(521\) | −20447.1 | −1.71939 | −0.859695 | − | 0.510808i | \(-0.829346\pi\) | ||||
−0.859695 | + | 0.510808i | \(0.829346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20329.0 | 1.69967 | 0.849833 | − | 0.527052i | \(-0.176703\pi\) | ||||
0.849833 | + | 0.527052i | \(0.176703\pi\) | |||||||
\(524\) | −2298.02 | −0.191583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16074.9 | −1.33251 | ||||||||
\(527\) | −10183.9 | −0.841776 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11959.9 | −0.982976 | ||||||||
\(530\) | −27422.3 | −2.24745 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −380.824 | −0.0310353 | ||||||||
\(533\) | 10128.3 | 0.823087 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24369.9 | −1.96935 | ||||||||
\(536\) | −1419.76 | −0.114411 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7784.41 | 0.623810 | ||||||||
\(539\) | 19085.5 | 1.52518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14893.6 | −1.18360 | −0.591799 | − | 0.806085i | \(-0.701582\pi\) | ||||
−0.591799 | + | 0.806085i | \(0.701582\pi\) | |||||||
\(542\) | −13125.8 | −1.04022 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10247.5 | 0.807646 | ||||||||
\(545\) | −13748.8 | −1.08062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12312.0 | −0.962383 | −0.481192 | − | 0.876615i | \(-0.659796\pi\) | ||||
−0.481192 | + | 0.876615i | \(0.659796\pi\) | |||||||
\(548\) | 3640.64 | 0.283796 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15196.7 | 1.17816 | ||||||||
\(551\) | 388.763 | 0.0300578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7230.70 | 0.556022 | ||||||||
\(554\) | 30937.0 | 2.37254 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11350.7 | −0.865787 | ||||||||
\(557\) | 8573.98 | 0.652229 | 0.326114 | − | 0.945330i | \(-0.394261\pi\) | ||||
0.326114 | + | 0.945330i | \(0.394261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2248.95 | 0.170162 | ||||||||
\(560\) | 7948.25 | 0.599776 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6686.36 | 0.501863 | ||||||||
\(563\) | −6372.85 | −0.477058 | −0.238529 | − | 0.971135i | \(-0.576665\pi\) | ||||
−0.238529 | + | 0.971135i | \(0.576665\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12838.3 | 0.955947 | ||||||||
\(566\) | −26818.5 | −1.99163 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1651.59 | 0.122006 | ||||||||
\(569\) | 6730.36 | 0.495873 | 0.247936 | − | 0.968776i | \(-0.420248\pi\) | ||||
0.247936 | + | 0.968776i | \(0.420248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8502.34 | 0.623138 | 0.311569 | − | 0.950224i | \(-0.399145\pi\) | ||||
0.311569 | + | 0.950224i | \(0.399145\pi\) | |||||||
\(572\) | −9224.34 | −0.674281 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10227.6 | −0.743716 | ||||||||
\(575\) | −908.484 | −0.0658894 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2908.85 | 0.209874 | 0.104937 | − | 0.994479i | \(-0.466536\pi\) | ||||
0.104937 | + | 0.994479i | \(0.466536\pi\) | |||||||
\(578\) | 8795.72 | 0.632965 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2838.29 | 0.203196 | ||||||||
\(581\) | 6895.66 | 0.492393 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36356.0 | 2.58269 | ||||||||
\(584\) | −8340.06 | −0.590949 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3467.53 | 0.244441 | ||||||||
\(587\) | −17116.3 | −1.20352 | −0.601760 | − | 0.798677i | \(-0.705534\pi\) | ||||
−0.601760 | + | 0.798677i | \(0.705534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2006.43 | 0.140362 | ||||||||
\(590\) | −18724.7 | −1.30658 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30320.6 | −2.10502 | ||||||||
\(593\) | −17817.9 | −1.23389 | −0.616943 | − | 0.787008i | \(-0.711629\pi\) | ||||
−0.616943 | + | 0.787008i | \(0.711629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5060.41 | −0.348667 | ||||||||
\(596\) | −678.863 | −0.0466566 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1393.51 | 0.0952922 | ||||||||
\(599\) | −21014.6 | −1.43344 | −0.716722 | − | 0.697359i | \(-0.754358\pi\) | ||||
−0.716722 | + | 0.697359i | \(0.754358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24286.8 | −1.64839 | −0.824194 | − | 0.566308i | \(-0.808371\pi\) | ||||
−0.824194 | + | 0.566308i | \(0.808371\pi\) | |||||||
\(602\) | −2271.01 | −0.153753 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5694.46 | 0.383617 | ||||||||
\(605\) | −41788.2 | −2.80815 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3487.33 | 0.233190 | 0.116595 | − | 0.993180i | \(-0.462802\pi\) | ||||
0.116595 | + | 0.993180i | \(0.462802\pi\) | |||||||
\(608\) | −2018.97 | −0.134671 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23031.4 | 1.52871 | ||||||||
\(611\) | −2113.97 | −0.139971 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3348.02 | −0.220596 | −0.110298 | − | 0.993899i | \(-0.535180\pi\) | ||||
−0.110298 | + | 0.993899i | \(0.535180\pi\) | |||||||
\(614\) | 3454.42 | 0.227051 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4908.95 | −0.321083 | ||||||||
\(617\) | −415.752 | −0.0271273 | −0.0135636 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135636 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20765.7 | −1.34837 | −0.674187 | − | 0.738561i | \(-0.735506\pi\) | ||||
−0.674187 | + | 0.738561i | \(0.735506\pi\) | |||||||
\(620\) | 14648.6 | 0.948871 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21529.4 | 1.38787 | ||||||||
\(623\) | 4778.74 | 0.307313 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19530.9 | −1.24998 | ||||||||
\(626\) | −3922.95 | −0.250467 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4403.91 | −0.279833 | ||||||||
\(629\) | 19304.3 | 1.22371 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18583.1 | 1.17239 | 0.586197 | − | 0.810168i | \(-0.300624\pi\) | ||||
0.586197 | + | 0.810168i | \(0.300624\pi\) | |||||||
\(632\) | 9835.55 | 0.619046 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23360.4 | 1.46335 | ||||||||
\(635\) | 918.545 | 0.0574037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7676.12 | −0.477455 | ||||||||
\(638\) | −9509.01 | −0.590071 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16586.6 | 1.02444 | ||||||||
\(641\) | 10050.2 | 0.619279 | 0.309639 | − | 0.950854i | \(-0.399792\pi\) | ||||
0.309639 | + | 0.950854i | \(0.399792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27887.6 | −1.71039 | −0.855193 | − | 0.518310i | \(-0.826561\pi\) | ||||
−0.855193 | + | 0.518310i | \(0.826561\pi\) | |||||||
\(644\) | −556.855 | −0.0340732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1789.03 | 0.108961 | ||||||||
\(647\) | −17596.4 | −1.06922 | −0.534610 | − | 0.845099i | \(-0.679542\pi\) | ||||
−0.534610 | + | 0.845099i | \(0.679542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24824.8 | 1.50148 | ||||||||
\(650\) | −6112.07 | −0.368823 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7590.31 | 0.455920 | ||||||||
\(653\) | −7842.61 | −0.469993 | −0.234996 | − | 0.971996i | \(-0.575508\pi\) | ||||
−0.234996 | + | 0.971996i | \(0.575508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6016.26 | 0.358893 | ||||||||
\(656\) | −29864.1 | −1.77743 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2134.71 | 0.126473 | ||||||||
\(659\) | −3967.06 | −0.234499 | −0.117249 | − | 0.993102i | \(-0.537408\pi\) | ||||
−0.117249 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13012.7 | 0.765710 | 0.382855 | − | 0.923808i | \(-0.374941\pi\) | ||||
0.382855 | + | 0.923808i | \(0.374941\pi\) | |||||||
\(662\) | 7901.68 | 0.463908 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9379.82 | 0.548204 | ||||||||
\(665\) | 997.004 | 0.0581386 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 568.464 | 0.0330000 | ||||||||
\(668\) | 15411.0 | 0.892622 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7053.02 | −0.406689 | ||||||||
\(671\) | −30534.7 | −1.75675 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22159.3 | 1.26921 | 0.634605 | − | 0.772837i | \(-0.281163\pi\) | ||||
0.634605 | + | 0.772837i | \(0.281163\pi\) | |||||||
\(674\) | 16265.4 | 0.929555 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7800.11 | −0.443793 | ||||||||
\(677\) | −16452.8 | −0.934019 | −0.467010 | − | 0.884252i | \(-0.654669\pi\) | ||||
−0.467010 | + | 0.884252i | \(0.654669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4131.79 | 0.233525 | ||||||||
\(680\) | −6883.43 | −0.388187 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −49076.5 | −2.75548 | ||||||||
\(683\) | −6703.67 | −0.375562 | −0.187781 | − | 0.982211i | \(-0.560130\pi\) | ||||
−0.187781 | + | 0.982211i | \(0.560130\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9531.26 | −0.531636 | ||||||||
\(686\) | 16968.5 | 0.944405 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6631.22 | −0.367460 | ||||||||
\(689\) | −14622.3 | −0.808511 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23807.8 | 1.31069 | 0.655347 | − | 0.755328i | \(-0.272522\pi\) | ||||
0.655347 | + | 0.755328i | \(0.272522\pi\) | |||||||
\(692\) | 4868.55 | 0.267449 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1003.39 | 0.0548821 | ||||||||
\(695\) | 29716.4 | 1.62188 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19013.6 | 1.03327 | ||||||||
\(698\) | 22964.5 | 1.24530 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2442.43 | 0.131879 | ||||||||
\(701\) | 15905.9 | 0.856999 | 0.428499 | − | 0.903542i | \(-0.359042\pi\) | ||||
0.428499 | + | 0.903542i | \(0.359042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3803.33 | −0.204047 | ||||||||
\(704\) | 7850.82 | 0.420297 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1647.16 | 0.0878069 | ||||||||
\(707\) | 7902.90 | 0.420395 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19476.5 | 1.03167 | 0.515836 | − | 0.856687i | \(-0.327481\pi\) | ||||
0.515836 | + | 0.856687i | \(0.327481\pi\) | |||||||
\(710\) | 8204.69 | 0.433685 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6500.27 | 0.342146 | ||||||||
\(713\) | 2933.87 | 0.154102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24149.5 | 1.26313 | ||||||||
\(716\) | 20858.7 | 1.08872 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.7362 | 0.000921877 0 | ||||||||
\(719\) | −19269.8 | −0.999504 | −0.499752 | − | 0.866168i | \(-0.666576\pi\) | ||||
−0.499752 | + | 0.866168i | \(0.666576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9307.24 | −0.480749 | ||||||||
\(722\) | 24604.3 | 1.26825 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2449.12 | 0.125719 | ||||||||
\(725\) | −2493.35 | −0.127725 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18301.4 | 0.933645 | 0.466823 | − | 0.884351i | \(-0.345399\pi\) | ||||
0.466823 | + | 0.884351i | \(0.345399\pi\) | |||||||
\(728\) | 1974.37 | 0.100515 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41431.2 | −2.10060 | ||||||||
\(731\) | 4221.90 | 0.213615 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16411.7 | 0.826986 | 0.413493 | − | 0.910507i | \(-0.364309\pi\) | ||||
0.413493 | + | 0.910507i | \(0.364309\pi\) | |||||||
\(734\) | 48452.1 | 2.43651 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2952.22 | −0.147853 | ||||||||
\(737\) | 9350.77 | 0.467354 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27984.1 | 1.39298 | 0.696489 | − | 0.717568i | \(-0.254745\pi\) | ||||
0.696489 | + | 0.717568i | \(0.254745\pi\) | |||||||
\(740\) | −27767.4 | −1.37939 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14765.7 | 0.730547 | ||||||||
\(743\) | 8620.47 | 0.425645 | 0.212823 | − | 0.977091i | \(-0.431734\pi\) | ||||
0.212823 | + | 0.977091i | \(0.431734\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1777.28 | 0.0874019 | ||||||||
\(746\) | 25693.2 | 1.26099 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17316.6 | −0.846468 | ||||||||
\(749\) | 13122.1 | 0.640150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26617.5 | 1.29333 | 0.646663 | − | 0.762776i | \(-0.276164\pi\) | ||||
0.646663 | + | 0.762776i | \(0.276164\pi\) | |||||||
\(752\) | 6233.21 | 0.302263 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3824.50 | 0.184721 | ||||||||
\(755\) | −14908.2 | −0.718630 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18198.8 | 0.873775 | 0.436888 | − | 0.899516i | \(-0.356081\pi\) | ||||
0.436888 | + | 0.899516i | \(0.356081\pi\) | |||||||
\(758\) | −49257.5 | −2.36031 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1356.17 | 0.0647284 | ||||||||
\(761\) | −7352.93 | −0.350254 | −0.175127 | − | 0.984546i | \(-0.556034\pi\) | ||||
−0.175127 | + | 0.984546i | \(0.556034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7403.15 | 0.351261 | ||||||||
\(764\) | 1320.27 | 0.0625207 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22792.2 | 1.07509 | ||||||||
\(767\) | −9984.48 | −0.470038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24387.8 | 1.14362 | 0.571811 | − | 0.820385i | \(-0.306241\pi\) | ||||
0.571811 | + | 0.820385i | \(0.306241\pi\) | |||||||
\(770\) | −24386.4 | −1.14133 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18731.3 | −0.873259 | ||||||||
\(773\) | 6489.66 | 0.301962 | 0.150981 | − | 0.988537i | \(-0.451757\pi\) | ||||
0.150981 | + | 0.988537i | \(0.451757\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12868.3 | −0.596442 | ||||||||
\(776\) | 5620.27 | 0.259995 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24467.1 | −1.12749 | ||||||||
\(779\) | −3746.06 | −0.172293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10877.6 | −0.498377 | ||||||||
\(782\) | 2615.99 | 0.119626 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22633.7 | 1.03105 | ||||||||
\(785\) | 11529.5 | 0.524212 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11896.6 | −0.538840 | −0.269420 | − | 0.963023i | \(-0.586832\pi\) | ||||
−0.269420 | + | 0.963023i | \(0.586832\pi\) | |||||||
\(788\) | −28680.1 | −1.29656 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 48860.4 | 2.20048 | ||||||||
\(791\) | −6912.85 | −0.310736 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12281.0 | 0.549950 | ||||||||
\(794\) | −16658.4 | −0.744565 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22929.9 | 1.02102 | ||||||||
\(797\) | 13147.1 | 0.584310 | 0.292155 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292155 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3968.50 | −0.175714 | ||||||||
\(800\) | 12948.8 | 0.572259 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1088.80 | 0.0479389 | ||||||||
\(803\) | 54928.8 | 2.41394 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1457.86 | 0.0638295 | ||||||||
\(806\) | 19738.4 | 0.862601 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10749.9 | 0.468046 | ||||||||
\(809\) | −27417.7 | −1.19154 | −0.595770 | − | 0.803155i | \(-0.703153\pi\) | ||||
−0.595770 | + | 0.803155i | \(0.703153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26093.5 | −1.12980 | −0.564899 | − | 0.825160i | \(-0.691085\pi\) | ||||
−0.564899 | + | 0.825160i | \(0.691085\pi\) | |||||||
\(812\) | −1528.30 | −0.0660501 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 93028.2 | 4.00569 | ||||||||
\(815\) | −19871.6 | −0.854076 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −831.800 | −0.0356193 | ||||||||
\(818\) | −8422.55 | −0.360009 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27349.3 | −1.16473 | ||||||||
\(821\) | −7728.72 | −0.328544 | −0.164272 | − | 0.986415i | \(-0.552527\pi\) | ||||
−0.164272 | + | 0.986415i | \(0.552527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1290.35 | 0.0546521 | 0.0273260 | − | 0.999627i | \(-0.491301\pi\) | ||||
0.0273260 | + | 0.999627i | \(0.491301\pi\) | |||||||
\(824\) | −12660.2 | −0.535240 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10082.4 | 0.424712 | ||||||||
\(827\) | −6519.87 | −0.274145 | −0.137073 | − | 0.990561i | \(-0.543769\pi\) | ||||
−0.137073 | + | 0.990561i | \(0.543769\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45033.9 | −1.88672 | −0.943361 | − | 0.331768i | \(-0.892355\pi\) | ||||
−0.943361 | + | 0.331768i | \(0.892355\pi\) | |||||||
\(830\) | 46596.5 | 1.94866 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3157.58 | −0.131574 | ||||||||
\(833\) | −14410.2 | −0.599380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40346.4 | −1.67215 | ||||||||
\(836\) | 3411.72 | 0.141145 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 50172.0 | 2.06821 | ||||||||
\(839\) | −6258.20 | −0.257517 | −0.128759 | − | 0.991676i | \(-0.541099\pi\) | ||||
−0.128759 | + | 0.991676i | \(0.541099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22828.8 | −0.936030 | ||||||||
\(842\) | 22443.6 | 0.918595 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7192.10 | 0.293320 | ||||||||
\(845\) | 20420.9 | 0.831360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22501.1 | 0.912807 | ||||||||
\(848\) | 43114.9 | 1.74596 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11474.0 | −0.463007 | ||||||||
\(851\) | −5561.38 | −0.224021 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44415.9 | 1.78285 | 0.891424 | − | 0.453169i | \(-0.149707\pi\) | ||||
0.891424 | + | 0.453169i | \(0.149707\pi\) | |||||||
\(854\) | −12401.4 | −0.496918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17849.4 | 0.712709 | ||||||||
\(857\) | 36097.5 | 1.43882 | 0.719409 | − | 0.694587i | \(-0.244413\pi\) | ||||
0.719409 | + | 0.694587i | \(0.244413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44430.9 | 1.76480 | 0.882399 | − | 0.470501i | \(-0.155927\pi\) | ||||
0.882399 | + | 0.470501i | \(0.155927\pi\) | |||||||
\(860\) | −6072.82 | −0.240792 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17608.4 | 0.695759 | ||||||||
\(863\) | 6970.04 | 0.274928 | 0.137464 | − | 0.990507i | \(-0.456105\pi\) | ||||
0.137464 | + | 0.990507i | \(0.456105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12746.0 | −0.501013 | ||||||||
\(866\) | −19195.3 | −0.753214 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7887.61 | −0.308437 | ||||||||
\(869\) | −64778.4 | −2.52872 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3760.86 | −0.146305 | ||||||||
\(872\) | 10070.1 | 0.391075 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −515.404 | −0.0199471 | ||||||||
\(875\) | 6267.79 | 0.242160 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20920.2 | 0.805500 | 0.402750 | − | 0.915310i | \(-0.368054\pi\) | ||||
0.402750 | + | 0.915310i | \(0.368054\pi\) | |||||||
\(878\) | 29198.0 | 1.12231 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −71206.7 | −2.72770 | ||||||||
\(881\) | 44357.8 | 1.69631 | 0.848157 | − | 0.529746i | \(-0.177713\pi\) | ||||
0.848157 | + | 0.529746i | \(0.177713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25872.0 | −0.986028 | −0.493014 | − | 0.870021i | \(-0.664105\pi\) | ||||
−0.493014 | + | 0.870021i | \(0.664105\pi\) | |||||||
\(884\) | 6964.69 | 0.264986 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36473.5 | 1.38301 | ||||||||
\(887\) | −1291.93 | −0.0489052 | −0.0244526 | − | 0.999701i | \(-0.507784\pi\) | ||||
−0.0244526 | + | 0.999701i | \(0.507784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −494.597 | −0.0186594 | ||||||||
\(890\) | 32291.7 | 1.21620 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4248.10 | −0.159458 | ||||||||
\(893\) | 781.876 | 0.0292995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54608.5 | −2.03951 | ||||||||
\(896\) | −8931.18 | −0.333002 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42301.6 | 1.57196 | ||||||||
\(899\) | 8052.05 | 0.298722 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27450.0 | −1.01497 | ||||||||
\(902\) | 91627.3 | 3.38232 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9403.20 | −0.345958 | ||||||||
\(905\) | −6411.85 | −0.235511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2998.23 | 0.109762 | 0.0548812 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548812 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(908\) | 17578.4 | 0.642466 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9808.13 | 0.357293 | ||||||||
\(911\) | −10463.1 | −0.380524 | −0.190262 | − | 0.981733i | \(-0.560934\pi\) | ||||
−0.190262 | + | 0.981733i | \(0.560934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61776.9 | −2.23934 | ||||||||
\(914\) | −31179.4 | −1.12836 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16377.2 | −0.590739 | ||||||||
\(917\) | −3239.49 | −0.116660 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50998.5 | 1.83056 | 0.915280 | − | 0.402818i | \(-0.131969\pi\) | ||||
0.915280 | + | 0.402818i | \(0.131969\pi\) | |||||||
\(920\) | 1983.05 | 0.0710644 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 57774.3 | 2.06366 | ||||||||
\(923\) | 4374.96 | 0.156017 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24392.8 | 0.867060 | ||||||||
\(926\) | −41236.9 | −1.46342 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8102.40 | −0.286610 | ||||||||
\(929\) | 9821.02 | 0.346843 | 0.173421 | − | 0.984848i | \(-0.444518\pi\) | ||||
0.173421 | + | 0.984848i | \(0.444518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2839.10 | 0.0999438 | ||||||||
\(932\) | −15602.1 | −0.548351 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22069.3 | −0.773159 | ||||||||
\(935\) | 45335.2 | 1.58569 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25597.2 | 0.892449 | 0.446225 | − | 0.894921i | \(-0.352768\pi\) | ||||
0.446225 | + | 0.894921i | \(0.352768\pi\) | |||||||
\(938\) | 3797.74 | 0.132197 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5708.33 | 0.198069 | ||||||||
\(941\) | 51229.7 | 1.77475 | 0.887375 | − | 0.461049i | \(-0.152527\pi\) | ||||
0.887375 | + | 0.461049i | \(0.152527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5477.63 | −0.189158 | ||||||||
\(944\) | 29440.0 | 1.01503 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20345.5 | 0.699250 | ||||||||
\(947\) | 8813.28 | 0.302422 | 0.151211 | − | 0.988502i | \(-0.451683\pi\) | ||||
0.151211 | + | 0.988502i | \(0.451683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22092.2 | −0.755684 | ||||||||
\(950\) | 2260.62 | 0.0772043 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3706.43 | 0.126183 | ||||||||
\(953\) | −41702.5 | −1.41750 | −0.708749 | − | 0.705460i | \(-0.750740\pi\) | ||||
−0.708749 | + | 0.705460i | \(0.750740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3456.51 | −0.117120 | ||||||||
\(956\) | −1252.12 | −0.0423605 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18977.0 | −0.639999 | ||||||||
\(959\) | 5132.17 | 0.172812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11766.1 | 0.394953 | ||||||||
\(962\) | −37415.7 | −1.25398 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16391.7 | −0.547658 | ||||||||
\(965\) | 49039.1 | 1.63588 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49400.1 | −1.64281 | −0.821407 | − | 0.570342i | \(-0.806811\pi\) | ||||
−0.821407 | + | 0.570342i | \(0.806811\pi\) | |||||||
\(968\) | 30607.1 | 1.01627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27920.0 | 0.924183 | ||||||||
\(971\) | 51272.8 | 1.69456 | 0.847282 | − | 0.531143i | \(-0.178237\pi\) | ||||
0.847282 | + | 0.531143i | \(0.178237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16001.0 | −0.527203 | ||||||||
\(974\) | 56649.8 | 1.86363 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36211.4 | −1.18760 | ||||||||
\(977\) | −4073.15 | −0.133379 | −0.0666896 | − | 0.997774i | \(-0.521244\pi\) | ||||
−0.0666896 | + | 0.997774i | \(0.521244\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42811.8 | −1.39762 | ||||||||
\(980\) | 20727.7 | 0.675636 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4678.04 | 0.152019 | ||||||||
\(983\) | −27220.7 | −0.883219 | −0.441609 | − | 0.897207i | \(-0.645592\pi\) | ||||
−0.441609 | + | 0.897207i | \(0.645592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 75085.2 | 2.42885 | ||||||||
\(986\) | 7179.63 | 0.231892 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1372.19 | −0.0441852 | ||||||||
\(989\) | −1216.29 | −0.0391059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57200.3 | 1.83353 | 0.916765 | − | 0.399428i | \(-0.130791\pi\) | ||||
0.916765 | + | 0.399428i | \(0.130791\pi\) | |||||||
\(992\) | −41816.9 | −1.33840 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4417.87 | −0.140972 | ||||||||
\(995\) | −60030.9 | −1.91267 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14610.2 | −0.464103 | −0.232051 | − | 0.972704i | \(-0.574544\pi\) | ||||
−0.232051 | + | 0.972704i | \(0.574544\pi\) | |||||||
\(998\) | −8527.36 | −0.270470 | ||||||||
\(999\) | 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 | 2151.4.a.d.1.9 | 32 | ||
3.2 | odd | 2 | 717.4.a.d.1.24 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.d.1.24 | ✓ | 32 | 3.2 | odd | 2 | ||
2151.4.a.d.1.9 | 32 | 1.1 | even | 1 | trivial |