Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,4,Mod(1,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1960.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.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: | \(115.643743611\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1960.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.192450 | 0.0962250 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962250 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.0000 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.0000 | 0.362689 | 0.181344 | − | 0.983420i | \(-0.441955\pi\) | ||||
0.181344 | + | 0.983420i | \(0.441955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.00000 | −0.0860663 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0000 | 0.214002 | 0.107001 | − | 0.994259i | \(-0.465875\pi\) | ||||
0.107001 | + | 0.994259i | \(0.465875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −74.0000 | −0.893514 | −0.446757 | − | 0.894655i | \(-0.647421\pi\) | ||||
−0.446757 | + | 0.894655i | \(0.647421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14.0000 | −0.126922 | −0.0634609 | − | 0.997984i | \(-0.520214\pi\) | ||||
−0.0634609 | + | 0.997984i | \(0.520214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.0000 | −0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −237.000 | −1.51758 | −0.758790 | − | 0.651336i | \(-0.774209\pi\) | ||||
−0.758790 | + | 0.651336i | \(0.774209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 180.000 | 1.04287 | 0.521435 | − | 0.853291i | \(-0.325397\pi\) | ||||
0.521435 | + | 0.853291i | \(0.325397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −39.0000 | −0.205728 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −318.000 | −1.41294 | −0.706471 | − | 0.707742i | \(-0.749714\pi\) | ||||
−0.706471 | + | 0.707742i | \(0.749714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.0000 | 0.0697995 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 348.000 | 1.32557 | 0.662786 | − | 0.748809i | \(-0.269374\pi\) | ||||
0.662786 | + | 0.748809i | \(0.269374\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.0000 | −0.0780225 | −0.0390113 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390113 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 130.000 | 0.430650 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 193.000 | 0.598978 | 0.299489 | − | 0.954100i | \(-0.403184\pi\) | ||||
0.299489 | + | 0.954100i | \(0.403184\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.0000 | 0.0411847 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −208.000 | −0.539075 | −0.269538 | − | 0.962990i | \(-0.586871\pi\) | ||||
−0.269538 | + | 0.962990i | \(0.586871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 195.000 | 0.478069 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −74.0000 | −0.171957 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −452.000 | −0.997379 | −0.498690 | − | 0.866781i | \(-0.666185\pi\) | ||||
−0.498690 | + | 0.866781i | \(0.666185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −340.000 | −0.713648 | −0.356824 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356824 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −85.0000 | −0.162199 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −408.000 | −0.743957 | −0.371979 | − | 0.928241i | \(-0.621321\pi\) | ||||
−0.371979 | + | 0.928241i | \(0.621321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.0000 | −0.0244261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 528.000 | 0.882564 | 0.441282 | − | 0.897368i | \(-0.354524\pi\) | ||||
0.441282 | + | 0.897368i | \(0.354524\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 554.000 | 0.888230 | 0.444115 | − | 0.895970i | \(-0.353518\pi\) | ||||
0.444115 | + | 0.895970i | \(0.353518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.0000 | 0.0384900 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 539.000 | 0.767623 | 0.383812 | − | 0.923411i | \(-0.374611\pi\) | ||||
0.383812 | + | 0.923411i | \(0.374611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −164.000 | −0.216884 | −0.108442 | − | 0.994103i | \(-0.534586\pi\) | ||||
−0.108442 | + | 0.994103i | \(0.534586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −75.0000 | −0.0957046 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −237.000 | −0.292058 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 576.000 | 0.686021 | 0.343011 | − | 0.939332i | \(-0.388553\pi\) | ||||
0.343011 | + | 0.939332i | \(0.388553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 180.000 | 0.200700 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 370.000 | 0.399592 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 827.000 | 0.865661 | 0.432831 | − | 0.901475i | \(-0.357515\pi\) | ||||
0.432831 | + | 0.901475i | \(0.357515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1014.00 | 1.02940 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1114.00 | 1.09750 | 0.548748 | − | 0.835988i | \(-0.315105\pi\) | ||||
0.548748 | + | 0.835988i | \(0.315105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1643.00 | −1.57174 | −0.785872 | − | 0.618389i | \(-0.787785\pi\) | ||||
−0.785872 | + | 0.618389i | \(0.787785\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 710.000 | 0.641479 | 0.320740 | − | 0.947167i | \(-0.396069\pi\) | ||||
0.320740 | + | 0.947167i | \(0.396069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1321.00 | 1.16082 | 0.580408 | − | 0.814326i | \(-0.302893\pi\) | ||||
0.580408 | + | 0.814326i | \(0.302893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −318.000 | −0.271921 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 342.000 | 0.284714 | 0.142357 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142357 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 70.0000 | 0.0567612 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −442.000 | −0.349256 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.000 | 0.142750 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 348.000 | 0.255107 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1348.00 | −0.941856 | −0.470928 | − | 0.882172i | \(-0.656081\pi\) | ||||
−0.470928 | + | 0.882172i | \(0.656081\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.0000 | −0.0150154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −238.000 | −0.158734 | −0.0793670 | − | 0.996845i | \(-0.525290\pi\) | ||||
−0.0793670 | + | 0.996845i | \(0.525290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 265.000 | 0.168945 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −776.000 | −0.483928 | −0.241964 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241964 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −326.000 | −0.198928 | −0.0994639 | − | 0.995041i | \(-0.531713\pi\) | ||||
−0.0994639 | + | 0.995041i | \(0.531713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 193.000 | 0.115273 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −663.000 | −0.387712 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1185.00 | 0.678682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3282.00 | 1.80451 | 0.902255 | − | 0.431203i | \(-0.141911\pi\) | ||||
0.902255 | + | 0.431203i | \(0.141911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2627.00 | 1.41578 | 0.707888 | − | 0.706325i | \(-0.249648\pi\) | ||||
0.707888 | + | 0.706325i | \(0.249648\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −390.000 | −0.206076 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −900.000 | −0.466385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −258.000 | −0.131151 | −0.0655753 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655753 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −208.000 | −0.103745 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 134.000 | 0.0643907 | 0.0321954 | − | 0.999482i | \(-0.489750\pi\) | ||||
0.0321954 | + | 0.999482i | \(0.489750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 195.000 | 0.0920044 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4181.00 | 1.93734 | 0.968669 | − | 0.248355i | \(-0.0798899\pi\) | ||||
0.968669 | + | 0.248355i | \(0.0798899\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1908.00 | −0.868457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1924.00 | 0.860421 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2901.00 | −1.27491 | −0.637454 | − | 0.770489i | \(-0.720012\pi\) | ||||
−0.637454 | + | 0.770489i | \(0.720012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −452.000 | −0.191946 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4404.00 | 1.83894 | 0.919470 | − | 0.393159i | \(-0.128618\pi\) | ||||
0.919470 | + | 0.393159i | \(0.128618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1752.00 | −0.719476 | −0.359738 | − | 0.933053i | \(-0.617134\pi\) | ||||
−0.359738 | + | 0.933053i | \(0.617134\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −340.000 | −0.137342 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1590.00 | 0.631887 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −585.000 | −0.228767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3595.00 | −1.36191 | −0.680956 | − | 0.732325i | \(-0.738435\pi\) | ||||
−0.680956 | + | 0.732325i | \(0.738435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3448.00 | 1.28597 | 0.642986 | − | 0.765878i | \(-0.277695\pi\) | ||||
0.642986 | + | 0.765878i | \(0.277695\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −85.0000 | −0.0312153 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3576.00 | −1.29330 | −0.646648 | − | 0.762788i | \(-0.723830\pi\) | ||||
−0.646648 | + | 0.762788i | \(0.723830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2868.00 | −1.02164 | −0.510822 | − | 0.859687i | \(-0.670659\pi\) | ||||
−0.510822 | + | 0.859687i | \(0.670659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −408.000 | −0.143175 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1740.00 | −0.592814 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 364.000 | 0.122221 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2886.00 | 0.955162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1359.00 | 0.443400 | 0.221700 | − | 0.975115i | \(-0.428839\pi\) | ||||
0.221700 | + | 0.975115i | \(0.428839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 528.000 | 0.169850 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 110.000 | 0.0348927 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 554.000 | 0.170940 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 255.000 | 0.0776161 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5693.00 | 1.70956 | 0.854779 | − | 0.518992i | \(-0.173693\pi\) | ||||
0.854779 | + | 0.518992i | \(0.173693\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −650.000 | −0.192593 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6381.00 | 1.86574 | 0.932868 | − | 0.360220i | \(-0.117298\pi\) | ||||
0.932868 | + | 0.360220i | \(0.117298\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3556.00 | −1.02614 | −0.513072 | − | 0.858345i | \(-0.671493\pi\) | ||||
−0.513072 | + | 0.858345i | \(0.671493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 872.000 | 0.245179 | 0.122589 | − | 0.992457i | \(-0.460880\pi\) | ||||
0.122589 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −965.000 | −0.267871 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 539.000 | 0.147729 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2129.00 | −0.576207 | −0.288104 | − | 0.957599i | \(-0.593025\pi\) | ||||
−0.288104 | + | 0.957599i | \(0.593025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −778.000 | −0.207948 | −0.103974 | − | 0.994580i | \(-0.533156\pi\) | ||||
−0.103974 | + | 0.994580i | \(0.533156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2080.00 | 0.549103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1258.00 | −0.324067 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −164.000 | −0.0417393 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4990.00 | 1.25484 | 0.627422 | − | 0.778679i | \(-0.284110\pi\) | ||||
0.627422 | + | 0.778679i | \(0.284110\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 546.000 | 0.135679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −75.0000 | −0.0184184 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3630.00 | 0.881063 | 0.440531 | − | 0.897737i | \(-0.354790\pi\) | ||||
0.440531 | + | 0.897737i | \(0.354790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6162.00 | 1.46137 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −290.000 | −0.0679930 | −0.0339965 | − | 0.999422i | \(-0.510824\pi\) | ||||
−0.0339965 | + | 0.999422i | \(0.510824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1040.00 | 0.241082 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 576.000 | 0.132025 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1854.00 | 0.420224 | 0.210112 | − | 0.977677i | \(-0.432617\pi\) | ||||
0.210112 | + | 0.977677i | \(0.432617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1836.00 | 0.411546 | 0.205773 | − | 0.978600i | \(-0.434029\pi\) | ||||
0.205773 | + | 0.978600i | \(0.434029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −975.000 | −0.213799 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6154.00 | 1.33487 | 0.667433 | − | 0.744670i | \(-0.267393\pi\) | ||||
0.667433 | + | 0.744670i | \(0.267393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4680.00 | −1.00424 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −437.000 | −0.0927731 | −0.0463865 | − | 0.998924i | \(-0.514771\pi\) | ||||
−0.0463865 | + | 0.998924i | \(0.514771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 347.000 | 0.0728870 | 0.0364435 | − | 0.999336i | \(-0.488397\pi\) | ||||
0.0364435 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 370.000 | 0.0769014 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4688.00 | −0.954203 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 827.000 | 0.166597 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1281.00 | −0.255416 | −0.127708 | − | 0.991812i | \(-0.540762\pi\) | ||||
−0.127708 | + | 0.991812i | \(0.540762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2260.00 | 0.446042 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2067.00 | 0.403837 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −238.000 | −0.0460331 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1114.00 | 0.211213 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1700.00 | 0.319153 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3611.00 | 0.671305 | 0.335653 | − | 0.941986i | \(-0.391043\pi\) | ||||
0.335653 | + | 0.941986i | \(0.391043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1643.00 | −0.302482 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8206.00 | 1.49620 | 0.748102 | − | 0.663584i | \(-0.230965\pi\) | ||||
0.748102 | + | 0.663584i | \(0.230965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4911.00 | −0.886857 | −0.443428 | − | 0.896310i | \(-0.646238\pi\) | ||||
−0.443428 | + | 0.896310i | \(0.646238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 606.000 | 0.107370 | 0.0536851 | − | 0.998558i | \(-0.482903\pi\) | ||||
0.0536851 | + | 0.998558i | \(0.482903\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9243.00 | 1.62228 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 710.000 | 0.123453 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1110.00 | −0.191214 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 425.000 | 0.0725377 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1321.00 | 0.223399 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5308.00 | 0.881432 | 0.440716 | − | 0.897647i | \(-0.354725\pi\) | ||||
0.440716 | + | 0.897647i | \(0.354725\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8268.00 | 1.36061 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2040.00 | 0.332708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10638.0 | −1.71955 | −0.859776 | − | 0.510672i | \(-0.829397\pi\) | ||||
−0.859776 | + | 0.510672i | \(0.829397\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 342.000 | 0.0547932 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7020.00 | −1.11482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 70.0000 | 0.0109237 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2194.00 | −0.339424 | −0.169712 | − | 0.985494i | \(-0.554284\pi\) | ||||
−0.169712 | + | 0.985494i | \(0.554284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −938.000 | −0.143868 | −0.0719341 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719341 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −901.000 | −0.137014 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4995.00 | 0.753136 | 0.376568 | − | 0.926389i | \(-0.377104\pi\) | ||||
0.376568 | + | 0.926389i | \(0.377104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2640.00 | −0.394695 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −752.000 | −0.110554 | −0.0552772 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552772 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1383.00 | −0.201633 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 190.000 | 0.0274722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2770.00 | −0.397229 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1175.00 | −0.167124 | −0.0835620 | − | 0.996503i | \(-0.526630\pi\) | ||||
−0.0835620 | + | 0.996503i | \(0.526630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9048.00 | −1.27648 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9520.00 | 1.32152 | 0.660760 | − | 0.750597i | \(-0.270234\pi\) | ||||
0.660760 | + | 0.750597i | \(0.270234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −125.000 | −0.0172133 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4029.00 | −0.550409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11620.0 | 1.57488 | 0.787440 | − | 0.616392i | \(-0.211406\pi\) | ||||
0.787440 | + | 0.616392i | \(0.211406\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1348.00 | −0.181260 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1708.00 | 0.227871 | 0.113936 | − | 0.993488i | \(-0.463654\pi\) | ||||
0.113936 | + | 0.993488i | \(0.463654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 572.000 | 0.0751328 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 125.000 | 0.0162924 | 0.00814621 | − | 0.999967i | \(-0.497407\pi\) | ||||
0.00814621 | + | 0.999967i | \(0.497407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −210.000 | −0.0271615 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −238.000 | −0.0305484 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2695.00 | −0.343292 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13077.0 | −1.65319 | −0.826594 | − | 0.562798i | \(-0.809725\pi\) | ||||
−0.826594 | + | 0.562798i | \(0.809725\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2161.00 | 0.269115 | 0.134558 | − | 0.990906i | \(-0.457039\pi\) | ||||
0.134558 | + | 0.990906i | \(0.457039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3060.00 | 0.378237 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3245.00 | −0.398137 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12402.0 | 1.51043 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9614.00 | 1.16230 | 0.581151 | − | 0.813796i | \(-0.302602\pi\) | ||||
0.581151 | + | 0.813796i | \(0.302602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −776.000 | −0.0931320 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 820.000 | 0.0969933 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −326.000 | −0.0382837 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8808.00 | −1.02697 | −0.513483 | − | 0.858100i | \(-0.671645\pi\) | ||||
−0.513483 | + | 0.858100i | \(0.671645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13207.0 | −1.52891 | −0.764453 | − | 0.644679i | \(-0.776991\pi\) | ||||
−0.764453 | + | 0.644679i | \(0.776991\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5018.00 | −0.576793 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 375.000 | 0.0428004 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −663.000 | −0.0746152 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13201.0 | 1.47534 | 0.737668 | − | 0.675164i | \(-0.235927\pi\) | ||||
0.737668 | + | 0.675164i | \(0.235927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11890.0 | 1.31962 | 0.659812 | − | 0.751431i | \(-0.270636\pi\) | ||||
0.659812 | + | 0.751431i | \(0.270636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1185.00 | 0.130612 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1036.00 | 0.113406 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4474.00 | −0.486406 | −0.243203 | − | 0.969975i | \(-0.578198\pi\) | ||||
−0.243203 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14302.0 | −1.53388 | −0.766940 | − | 0.641719i | \(-0.778221\pi\) | ||||
−0.766940 | + | 0.641719i | \(0.778221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2880.00 | −0.306798 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3282.00 | 0.347278 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9801.00 | −1.03015 | −0.515075 | − | 0.857145i | \(-0.672236\pi\) | ||||
−0.515075 | + | 0.857145i | \(0.672236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13572.0 | −1.41703 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2627.00 | 0.272466 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4968.00 | 0.508519 | 0.254260 | − | 0.967136i | \(-0.418168\pi\) | ||||
0.254260 | + | 0.967136i | \(0.418168\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −795.000 | −0.0808441 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9408.00 | 0.950486 | 0.475243 | − | 0.879854i | \(-0.342360\pi\) | ||||
0.475243 | + | 0.879854i | \(0.342360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1692.00 | −0.169836 | −0.0849178 | − | 0.996388i | \(-0.527063\pi\) | ||||
−0.0849178 | + | 0.996388i | \(0.527063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −900.000 | −0.0897559 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4199.00 | 0.416074 | 0.208037 | − | 0.978121i | \(-0.433293\pi\) | ||||
0.208037 | + | 0.978121i | \(0.433293\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −258.000 | −0.0252399 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 858.000 | 0.0834057 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1850.00 | −0.178703 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5408.00 | 0.519110 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −398.000 | −0.0379647 | −0.0189823 | − | 0.999820i | \(-0.506043\pi\) | ||||
−0.0189823 | + | 0.999820i | \(0.506043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5406.00 | −0.512458 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4135.00 | −0.387135 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13786.0 | 1.28276 | 0.641379 | − | 0.767224i | \(-0.278363\pi\) | ||||
0.641379 | + | 0.767224i | \(0.278363\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 134.000 | 0.0123920 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1891.00 | 0.173808 | 0.0869039 | − | 0.996217i | \(-0.472303\pi\) | ||||
0.0869039 | + | 0.996217i | \(0.472303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3555.00 | −0.324765 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5070.00 | −0.460363 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3171.00 | −0.284476 | −0.142238 | − | 0.989832i | \(-0.545430\pi\) | ||||
−0.142238 | + | 0.989832i | \(0.545430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4181.00 | 0.372841 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21803.0 | 1.93270 | 0.966350 | − | 0.257232i | \(-0.0828105\pi\) | ||||
0.966350 | + | 0.257232i | \(0.0828105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5570.00 | −0.490815 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1908.00 | −0.167135 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19174.0 | 1.66969 | 0.834845 | − | 0.550484i | \(-0.185557\pi\) | ||||
0.834845 | + | 0.550484i | \(0.185557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3922.00 | 0.337545 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8215.00 | 0.702905 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7527.00 | −0.640304 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2901.00 | −0.245356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3210.00 | 0.269928 | 0.134964 | − | 0.990850i | \(-0.456908\pi\) | ||||
0.134964 | + | 0.990850i | \(0.456908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3220.00 | 0.269218 | 0.134609 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134609 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2700.00 | 0.223176 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11971.0 | −0.983891 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11752.0 | 0.960439 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5916.00 | 0.480770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3550.00 | −0.286878 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4404.00 | 0.353904 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5443.00 | 0.432556 | 0.216278 | − | 0.976332i | \(-0.430608\pi\) | ||||
0.216278 | + | 0.976332i | \(0.430608\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1752.00 | −0.138463 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6605.00 | −0.519132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14988.0 | 1.17156 | 0.585778 | − | 0.810472i | \(-0.300789\pi\) | ||||
0.585778 | + | 0.810472i | \(0.300789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8840.00 | 0.687217 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17538.0 | 1.35598 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1590.00 | 0.121607 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3024.00 | −0.230038 | −0.115019 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115019 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −374.000 | −0.0282979 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −585.000 | −0.0440262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8964.00 | 0.671026 | 0.335513 | − | 0.942036i | \(-0.391090\pi\) | ||||
0.335513 | + | 0.942036i | \(0.391090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1710.00 | −0.127328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14022.0 | −1.03310 | −0.516549 | − | 0.856258i | \(-0.672784\pi\) | ||||
−0.516549 | + | 0.856258i | \(0.672784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20020.0 | −1.46727 | −0.733635 | − | 0.679544i | \(-0.762178\pi\) | ||||
−0.733635 | + | 0.679544i | \(0.762178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3595.00 | −0.262100 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −350.000 | −0.0253844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18349.0 | 1.32388 | 0.661940 | − | 0.749557i | \(-0.269733\pi\) | ||||
0.661940 | + | 0.749557i | \(0.269733\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3448.00 | 0.247485 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8112.00 | 0.576269 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2210.00 | 0.156192 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5616.00 | 0.394884 | 0.197442 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197442 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13320.0 | −0.931818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3576.00 | −0.248895 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8243.00 | −0.570825 | −0.285413 | − | 0.958405i | \(-0.592131\pi\) | ||||
−0.285413 | + | 0.958405i | \(0.592131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2868.00 | −0.196615 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4385.00 | 0.299109 | 0.149554 | − | 0.988753i | \(-0.452216\pi\) | ||||
0.149554 | + | 0.988753i | \(0.452216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14378.0 | −0.975858 | −0.487929 | − | 0.872883i | \(-0.662248\pi\) | ||||
−0.487929 | + | 0.872883i | \(0.662248\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10608.0 | 0.716403 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −950.000 | −0.0638397 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7235.00 | 0.483788 | 0.241894 | − | 0.970303i | \(-0.422231\pi\) | ||||
0.241894 | + | 0.970303i | \(0.422231\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3281.00 | 0.217242 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25350.0 | −1.67027 | −0.835136 | − | 0.550043i | \(-0.814611\pi\) | ||||
−0.835136 | + | 0.550043i | \(0.814611\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1740.00 | −0.114087 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4634.00 | −0.302363 | −0.151181 | − | 0.988506i | \(-0.548308\pi\) | ||||
−0.151181 | + | 0.988506i | \(0.548308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12446.0 | −0.808153 | −0.404077 | − | 0.914725i | \(-0.632407\pi\) | ||||
−0.404077 | + | 0.914725i | \(0.632407\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 742.000 | 0.0479476 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2886.00 | 0.183821 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4770.00 | −0.302373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7145.00 | 0.450773 | 0.225387 | − | 0.974269i | \(-0.427635\pi\) | ||||
0.225387 | + | 0.974269i | \(0.427635\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1359.00 | 0.0853324 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6740.00 | 0.421211 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13728.0 | −0.849877 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20846.0 | −1.28450 | −0.642252 | − | 0.766493i | \(-0.722000\pi\) | ||||
−0.642252 | + | 0.766493i | \(0.722000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1751.00 | −0.107391 | −0.0536957 | − | 0.998557i | \(-0.517100\pi\) | ||||
−0.0536957 | + | 0.998557i | \(0.517100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 110.000 | 0.00671511 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15016.0 | −0.912426 | −0.456213 | − | 0.889871i | \(-0.650795\pi\) | ||||
−0.456213 | + | 0.889871i | \(0.650795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17628.0 | 1.06619 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7902.00 | 0.473552 | 0.236776 | − | 0.971564i | \(-0.423909\pi\) | ||||
0.236776 | + | 0.971564i | \(0.423909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1190.00 | 0.0709880 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14404.0 | −0.855333 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10019.0 | −0.592238 | −0.296119 | − | 0.955151i | \(-0.595692\pi\) | ||||
−0.296119 | + | 0.955151i | \(0.595692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11456.0 | 0.674110 | 0.337055 | − | 0.941485i | \(-0.390569\pi\) | ||||
0.337055 | + | 0.941485i | \(0.390569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 255.000 | 0.0149372 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3318.00 | 0.192614 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5693.00 | 0.329005 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13260.0 | 0.762886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30912.0 | −1.77053 | −0.885267 | − | 0.465082i | \(-0.846025\pi\) | ||||
−0.885267 | + | 0.465082i | \(0.846025\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1325.00 | −0.0755545 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27839.0 | −1.58041 | −0.790207 | − | 0.612841i | \(-0.790027\pi\) | ||||
−0.790207 | + | 0.612841i | \(0.790027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6381.00 | 0.359061 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19996.0 | −1.12024 | −0.560121 | − | 0.828411i | \(-0.689245\pi\) | ||||
−0.560121 | + | 0.828411i | \(0.689245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3880.00 | 0.216419 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3556.00 | −0.197482 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3536.00 | −0.195517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4356.00 | −0.239812 | −0.119906 | − | 0.992785i | \(-0.538259\pi\) | ||||
−0.119906 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1630.00 | 0.0889632 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5220.00 | 0.283675 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 872.000 | 0.0471846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19327.0 | 1.04133 | 0.520664 | − | 0.853762i | \(-0.325684\pi\) | ||||
0.520664 | + | 0.853762i | \(0.325684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23532.0 | 1.26248 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −965.000 | −0.0515518 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6917.00 | −0.366394 | −0.183197 | − | 0.983076i | \(-0.558645\pi\) | ||||
−0.183197 | + | 0.983076i | \(0.558645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14014.0 | −0.739193 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2520.00 | −0.132363 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3315.00 | 0.173390 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2129.00 | −0.110891 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27106.0 | 1.40596 | 0.702979 | − | 0.711211i | \(-0.251853\pi\) | ||||
0.702979 | + | 0.711211i | \(0.251853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −778.000 | −0.0400195 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5925.00 | −0.303516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18024.0 | −0.919495 | −0.459748 | − | 0.888050i | \(-0.652060\pi\) | ||||
−0.459748 | + | 0.888050i | \(0.652060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −330.000 | −0.0166970 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5347.00 | −0.269435 | −0.134718 | − | 0.990884i | \(-0.543013\pi\) | ||||
−0.134718 | + | 0.990884i | \(0.543013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15912.0 | 0.795286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3833.00 | 0.190797 | 0.0953986 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0953986 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1258.00 | −0.0623668 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32120.0 | 1.58596 | 0.792980 | − | 0.609247i | \(-0.208528\pi\) | ||||
0.792980 | + | 0.609247i | \(0.208528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16410.0 | −0.807001 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4264.00 | 0.208851 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18859.0 | 0.916344 | 0.458172 | − | 0.888863i | \(-0.348504\pi\) | ||||
0.458172 | + | 0.888863i | \(0.348504\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4990.00 | 0.241495 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13135.0 | −0.633154 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26776.0 | 1.28559 | 0.642794 | − | 0.766039i | \(-0.277775\pi\) | ||||
0.642794 | + | 0.766039i | \(0.277775\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 546.000 | 0.0261114 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14722.0 | −0.701277 | −0.350639 | − | 0.936511i | \(-0.614035\pi\) | ||||
−0.350639 | + | 0.936511i | \(0.614035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1950.00 | 0.0921600 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7684.00 | −0.361738 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41042.0 | −1.92459 | −0.962297 | − | 0.272002i | \(-0.912314\pi\) | ||||
−0.962297 | + | 0.272002i | \(0.912314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3630.00 | 0.169561 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17735.0 | −0.825205 | −0.412603 | − | 0.910911i | \(-0.635380\pi\) | ||||
−0.412603 | + | 0.910911i | \(0.635380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4500.00 | 0.208574 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25752.0 | −1.18442 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20592.0 | −0.943457 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12561.0 | 0.573300 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1290.00 | 0.0586523 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43979.0 | −1.99197 | −0.995986 | − | 0.0895086i | \(-0.971470\pi\) | ||||
−0.995986 | + | 0.0895086i | \(0.971470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −290.000 | −0.0130853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5780.00 | −0.258832 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1040.00 | 0.0463962 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5301.00 | −0.235597 | −0.117799 | − | 0.993038i | \(-0.537584\pi\) | ||||
−0.117799 | + | 0.993038i | \(0.537584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2895.00 | 0.128182 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14976.0 | −0.660613 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21606.0 | −0.949513 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1854.00 | 0.0808722 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6737.00 | 0.292782 | 0.146391 | − | 0.989227i | \(-0.453234\pi\) | ||||
0.146391 | + | 0.989227i | \(0.453234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4366.00 | 0.189039 | 0.0945197 | − | 0.995523i | \(-0.469868\pi\) | ||||
0.0945197 | + | 0.995523i | \(0.469868\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1836.00 | 0.0792021 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −670.000 | −0.0287964 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1628.00 | 0.0697142 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36963.0 | −1.57128 | −0.785638 | − | 0.618686i | \(-0.787665\pi\) | ||||
−0.785638 | + | 0.618686i | \(0.787665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30924.0 | −1.30977 | −0.654886 | − | 0.755727i | \(-0.727284\pi\) | ||||
−0.654886 | + | 0.755727i | \(0.727284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −975.000 | −0.0411456 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1806.00 | −0.0759381 | −0.0379690 | − | 0.999279i | \(-0.512089\pi\) | ||||
−0.0379690 | + | 0.999279i | \(0.512089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12780.0 | −0.535426 | −0.267713 | − | 0.963499i | \(-0.586268\pi\) | ||||
−0.267713 | + | 0.963499i | \(0.586268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6154.00 | 0.256895 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20905.0 | −0.866404 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9540.00 | −0.393967 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20706.0 | −0.852027 | −0.426013 | − | 0.904717i | \(-0.640082\pi\) | ||||
−0.426013 | + | 0.904717i | \(0.640082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31780.0 | 1.30305 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −437.000 | −0.0178542 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9540.00 | 0.388386 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 347.000 | 0.0140271 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4452.00 | 0.179333 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20494.0 | 0.822627 | 0.411314 | − | 0.911494i | \(-0.365070\pi\) | ||||
0.411314 | + | 0.911494i | \(0.365070\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9620.00 | −0.384792 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36246.0 | −1.44474 | −0.722369 | − | 0.691508i | \(-0.756947\pi\) | ||||
−0.722369 | + | 0.691508i | \(0.756947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39596.0 | 1.57276 | 0.786378 | − | 0.617745i | \(-0.211954\pi\) | ||||
0.786378 | + | 0.617745i | \(0.211954\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16224.0 | −0.639944 | −0.319972 | − | 0.947427i | \(-0.603673\pi\) | ||||
−0.319972 | + | 0.947427i | \(0.603673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14505.0 | 0.570156 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4688.00 | −0.183636 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21021.0 | −0.820585 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6936.00 | −0.269825 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21502.0 | −0.833600 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11022.0 | 0.424386 | 0.212193 | − | 0.977228i | \(-0.431939\pi\) | ||||
0.212193 | + | 0.977228i | \(0.431939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1281.00 | −0.0491548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33600.0 | −1.28492 | −0.642459 | − | 0.766320i | \(-0.722086\pi\) | ||||
−0.642459 | + | 0.766320i | \(0.722086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43240.0 | 1.64795 | 0.823976 | − | 0.566625i | \(-0.191751\pi\) | ||||
0.823976 | + | 0.566625i | \(0.191751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2260.00 | 0.0858408 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3024.00 | −0.114471 | −0.0572356 | − | 0.998361i | \(-0.518229\pi\) | ||||
−0.0572356 | + | 0.998361i | \(0.518229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25311.0 | −0.951684 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14282.0 | −0.535195 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22020.0 | −0.822399 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −238.000 | −0.00885907 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42660.0 | −1.58264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3120.00 | −0.115363 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8760.00 | 0.321759 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40694.0 | −1.48977 | −0.744885 | − | 0.667192i | \(-0.767496\pi\) | ||||
−0.744885 | + | 0.667192i | \(0.767496\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28964.0 | −1.05685 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28728.0 | 1.04479 | 0.522394 | − | 0.852704i | \(-0.325039\pi\) | ||||
0.522394 | + | 0.852704i | \(0.325039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6396.00 | 0.231847 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1700.00 | 0.0614211 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9239.00 | 0.331628 | 0.165814 | − | 0.986157i | \(-0.446975\pi\) | ||||
0.165814 | + | 0.986157i | \(0.446975\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3611.00 | 0.129193 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8976.00 | 0.320096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7950.00 | −0.282589 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42718.0 | 1.51353 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30192.0 | −1.06627 | −0.533136 | − | 0.846029i | \(-0.678987\pi\) | ||||
−0.533136 | + | 0.846029i | \(0.678987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8206.00 | 0.287945 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2925.00 | 0.102308 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36515.0 | 1.27310 | 0.636549 | − | 0.771236i | \(-0.280361\pi\) | ||||
0.636549 | + | 0.771236i | \(0.280361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4911.00 | −0.170676 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46356.0 | 1.60591 | 0.802956 | − | 0.596039i | \(-0.203260\pi\) | ||||
0.802956 | + | 0.596039i | \(0.203260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4872.00 | −0.168244 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23800.0 | −0.816680 | −0.408340 | − | 0.912830i | \(-0.633892\pi\) | ||||
−0.408340 | + | 0.912830i | \(0.633892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9418.00 | 0.322151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 606.000 | 0.0206634 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44752.0 | 1.52115 | 0.760577 | − | 0.649248i | \(-0.224916\pi\) | ||||
0.760577 | + | 0.649248i | \(0.224916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17975.0 | 0.609065 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9243.00 | 0.312209 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2609.00 | 0.0875768 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18460.0 | −0.617721 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17240.0 | −0.575104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8870.00 | −0.294974 | −0.147487 | − | 0.989064i | \(-0.547118\pi\) | ||||
−0.147487 | + | 0.989064i | \(0.547118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1110.00 | −0.0367991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35616.0 | 1.17711 | 0.588554 | − | 0.808458i | \(-0.299697\pi\) | ||||
0.588554 | + | 0.808458i | \(0.299697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 425.000 | 0.0139599 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21894.0 | −0.716941 | −0.358470 | − | 0.933541i | \(-0.616702\pi\) | ||||
−0.358470 | + | 0.933541i | \(0.616702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22464.0 | −0.733353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34346.0 | −1.11782 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56037.0 | −1.81821 | −0.909106 | − | 0.416564i | \(-0.863234\pi\) | ||||
−0.909106 | + | 0.416564i | \(0.863234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17880.0 | 0.578380 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 308.000 | 0.00990276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13168.0 | 0.422094 | 0.211047 | − | 0.977476i | \(-0.432313\pi\) | ||||
0.211047 | + | 0.977476i | \(0.432313\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5308.00 | 0.169632 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14340.0 | 0.456893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24911.0 | 0.791313 | 0.395657 | − | 0.918399i | \(-0.370517\pi\) | ||||
0.395657 | + | 0.918399i | \(0.370517\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16854.0 | 0.533771 |
(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 | 1960.4.a.f.1.1 | 1 | ||
7.6 | odd | 2 | 280.4.a.b.1.1 | ✓ | 1 | ||
28.27 | even | 2 | 560.4.a.j.1.1 | 1 | |||
35.13 | even | 4 | 1400.4.g.g.449.1 | 2 | |||
35.27 | even | 4 | 1400.4.g.g.449.2 | 2 | |||
35.34 | odd | 2 | 1400.4.a.e.1.1 | 1 | |||
56.13 | odd | 2 | 2240.4.a.t.1.1 | 1 | |||
56.27 | even | 2 | 2240.4.a.q.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.4.a.b.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
560.4.a.j.1.1 | 1 | 28.27 | even | 2 | |||
1400.4.a.e.1.1 | 1 | 35.34 | odd | 2 | |||
1400.4.g.g.449.1 | 2 | 35.13 | even | 4 | |||
1400.4.g.g.449.2 | 2 | 35.27 | even | 4 | |||
1960.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2240.4.a.q.1.1 | 1 | 56.27 | even | 2 | |||
2240.4.a.t.1.1 | 1 | 56.13 | odd | 2 |